Publikationer av Henrik Shah Gholian
Refereegranskade
Artiklar
[1]
M. Fotouhi och H. Shahgholian, "A minimization problem with free boundary for p-Laplacian weakly coupled system," Advances in Nonlinear Analysis, vol. 13, no. 1, 2024.
[2]
S. Kim och H. Shahgholian, "Almost minimizers to a transmission problem for (p,q)-Laplacian," Nonlinear Analysis, vol. 241, 2024.
[3]
M. Colombo, S. Kim och H. Shahgholian, "A transmission problem with (p, q)-Laplacian," Communications in Partial Differential Equations, vol. 48, no. 2, s. 315-349, 2023.
[4]
D. De Silva, S. Jeon och H. Shahgholian, "Almost minimizers for a sublinear system with free boundary," Calculus of Variations and Partial Differential Equations, vol. 62, no. 5, 2023.
[5]
S. Eberle, H. Shahgholian och G. S. Weiss, "On Global Solutions of the Obstacle Problem," Duke mathematical journal, vol. 172, no. 11, s. 2149-2193, 2023.
[6]
A. Aghajani och H. Shahgholian, "Pointwise estimates for systems of coupled p-laplacian elliptic equations," Communications on Pure and Applied Analysis, vol. 22, no. 3, s. 899-921, 2023.
[7]
M. Allen, D. Kriventsov och H. Shahgholian, "The inhomogeneous boundary Harnack principle for fully nonlinear and p-Laplace equations," Annales de l'Institut Henri Poincare. Analyse non linéar, vol. 40, no. 1, s. 133-156, 2023.
[8]
S. Eberle, H. Shahgholian och G. S. Weiss, "The structure of the regular part of the free boundary close to singularities in the obstacle problem," Journal of Differential Equations, vol. 377, s. 873-887, 2023.
[9]
D. De Silva, S. Jeon och H. Shahgholian, "Almost minimizers for a singular system with free boundary," Journal of Differential Equations, vol. 336, s. 167-203, 2022.
[10]
D. De Silva, D. Jerison och H. Shahgholian, "Inhomogeneous global minimizers to the one-phase free boundary problem," Communications in Partial Differential Equations, vol. 47, no. 6, s. 1193-1216, 2022.
[11]
A. Figalli, S. Kim och H. Shahgholian, "Lipschitz regularity in vectorial linear transmission problems," Nonlinear Analysis, vol. 221, s. 112911, 2022.
[12]
D. Apushkinskaya, A. Petrosyan och H. Shahgholian, "Nina Nikolaevna Uraltseva," Notices of the American Mathematical Society, vol. 69, no. 03, s. 1-395, 2022.
[13]
P. Z. Kow et al., "Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena," Potential Analysis, 2022.
[14]
L. El Hajj och H. Shahgholian, "Quadrature identities with a background PDE," Analysis and Mathematical Physics, vol. 12, no. 2, 2022.
[15]
G. Aleksanyan et al., "Regularity of the free boundary for a parabolic cooperative system," Calculus of Variations and Partial Differential Equations, vol. 61, no. 4, 2022.
[16]
M. Fotouhi, H. Shahgholian och G. S. Weiss, "A free boundary problem for an elliptic system," Journal of Differential Equations, vol. 284, s. 126-155, 2021.
[17]
M. Salo och H. Shahgholian, "Free boundary methods and non-scattering phenomena," RESEARCH IN THE MATHEMATICAL SCIENCES, vol. 8, no. 4, 2021.
[18]
D. Kriventsov och H. Shahgholian, "Optimal regularity for a two-phase obstacle-like problem with logarithmic singularity," Communications in Partial Differential Equations, vol. 46, no. 10, s. 1831-1850, 2021.
[19]
L. El Hajj och H. Shahgholian, "REMARKS ON THE CONVEXITY OF FREE BOUNDARIES (SCALAR AND SYSTEM CASES)," St. Petersburg Mathematical Journal, vol. 32, no. 4, s. 713-727, 2021.
[20]
M. Ghergu, S. Kim och H. Shahgholian, "Isolated singularities for semilinear elliptic systems with power-law nonlinearity," Analysis & PDE, vol. 13, no. 3, s. 701-739, 2020.
[21]
M. Fazly och H. Shahgholian, "Monotonicity formulas for coupled elliptic gradient systems with applications," ADVANCES IN NONLINEAR ANALYSIS, vol. 9, no. 1, s. 479-495, 2020.
[22]
M. Fotouhi et al., "Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type," MATHEMATICS IN ENGINEERING, vol. 2, no. 4, s. 698-708, 2020.
[23]
R. Barkhudaryan et al., "System of variational inequalities with interconnected obstacles," Applicable Analysis, 2020.
[24]
M. Allen och H. Shahgholian, "A New Boundary Harnack Principle (Equations with Right Hand Side)," Archive for Rational Mechanics and Analysis, vol. 234, no. 3, s. 1413-1444, 2019.
[25]
H. Aleksanyan och H. Shahgholian, "Discrete balayage and boundary sandpile," Journal d'Analyse Mathematique, vol. 138, no. 1, s. 361-403, 2019.
[26]
M. Ghergu, S. Kim och H. Shahgholian, "Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity," ADVANCES IN NONLINEAR ANALYSIS, vol. 8, no. 1, s. 995-1003, 2019.
[27]
S. Kim, K.-A. Lee och H. Shahgholian, "HOMOGENIZATION OF THE BOUNDARY VALUE FOR THE DIRICHLET PROBLEM," Discrete and Continuous Dynamical Systems, vol. 39, no. 12, s. 6843-6864, 2019.
[28]
S. Kim och H. Shahgholian, "Homogenization of a Singular Perturbation Problem," Journal of Mathematical Sciences, vol. 242, no. 1, s. 163-176, 2019.
[29]
S. Kim, K.-A. Lee och H. Shahgholian, "Nodal Sets for "Broken" Quasilinear PDEs," Indiana University Mathematics Journal, vol. 68, no. 4, s. 1113-1148, 2019.
[30]
A. Arakelyan et al., "Numerical Treatment to a Non-local Parabolic Free Boundary Problem Arising in Financial Bubbles," Bulletin of the Iranian Mathematical Society, vol. 45, no. 1, s. 59-73, 2019.
[31]
H. Aleksanyan och H. Shahgholian, "Perturbed Divisible Sandpiles and Quadrature Surfaces," Potential Analysis, vol. 51, no. 4, s. 511-540, 2019.
[32]
K.-A. Lee, J. Park och H. Shahgholian, "The regularity theory for the double obstacle problem," Calculus of Variations and Partial Differential Equations, vol. 58, no. 3, 2019.
[33]
L. A. Caffarelli, H. Shahgholian och K. Yeressian, "A MINIMIZATION PROBLEM WITH FREE BOUNDARY RELATED TO A COOPERATIVE SYSTEM," Duke mathematical journal, vol. 167, no. 10, s. 1825-1882, 2018.
[34]
O. S. de Queiroz och H. Shahgholian, "A free boundary problem with log term singularity," Interfaces and free boundaries (Print), vol. 19, no. 3, s. 351-369, 2017.
[35]
M. Fotouhi och H. Shahgholian, "A semilinear PDE with free boundary," Nonlinear Analysis, Theory, Methods and Applications, vol. 151, s. 145-163, 2017.
[36]
S. Kim, K. -. Lee och H. Shahgholian, "An elliptic free boundary arising from the jump of conductivity," Nonlinear Analysis, vol. 161, s. 1-29, 2017.
[37]
A. L. Karakhanyan och H. Shahgholian, "On a conjecture of De Giorgi related to homogenization," Annali di Matematica Pura ed Applicata, vol. 196, no. 6, s. 2167-2183, 2017.
[38]
H. Shahgholian och K. Yeressian, "The obstacle problem with singular coefficients near Dirichlet data," Annales de l'Institut Henri Poincare. Analyse non linéar, vol. 34, no. 2, s. 293-334, 2017.
[39]
A. Arakelyan, H. Shahgholian och J. V. Prajapat, "Two-and multi-phase quadrature surfaces," Communications on Pure and Applied Analysis, vol. 16, no. 6, s. 2023-2045, 2017.
[40]
A. L. Karakhanyan och H. Shahgholian, "Boundary behaviour for a singular perturbation problem," Nonlinear Analysis, vol. 138, s. 176-188, 2016.
[41]
H. Aleksanyan, H. Shahgholian och P. Sjölin, "L2-estimates for singular oscillatory integral operators," Journal of Mathematical Analysis and Applications, vol. 441, no. 2, s. 529-548, 2016.
[42]
A. Arakelyan och H. Shah Gholian, "Multi-Phase Quadrature Domains and a Related Minimization Problem," Potential Analysis, s. 1-21, 2016.
[43]
H. Shah gholian, "REGULARITY ISSUES FOR SEMILINEAR PDE-S (A NARRATIVE APPROACH)," St. Petersburg Mathematical Journal, vol. 27, no. 3, s. 577-587, 2016.
[44]
A. Figalli och H. Shahgholian, "A general class of free boundary problems for fully nonlinear parabolic equations," Annali di Matematica Pura ed Applicata, vol. 194, no. 4, s. 1123-1134, 2015.
[45]
A. Figalli och H. Shahgholian, "An overview of unconstrained free boundary problems," Philosophical Transactions. Series A : Mathematical, physical, and engineering science, vol. 373, no. 2050, 2015.
[46]
A. L. Karakhanyan och H. Shahgholian, "Analysis of a free boundary at contact points with Lipschitz data," Transactions of the American Mathematical Society, vol. 367, no. 7, s. 5141-5175, 2015.
[47]
H. Aleksanyan, H. Shahgholian och P. Sjölin, "Applications of Fourier Analysis in Homogenization of the Dirichlet Problem : L-p Estimates," Archive for Rational Mechanics and Analysis, vol. 215, no. 1, s. 65-87, 2015.
[48]
J. Andersson et al., "Equilibrium points of a singular cooperative system with free boundary," Advances in Mathematics, vol. 280, s. 743-771, 2015.
[49]
H. Mikayelyan och H. Shah Gholian, "Hopf's lemma for a class of singular/degenerate PDE-S," Annales Academiae Scientiarum Fennicae Mathematica, vol. 40, no. 1, s. 475-484, 2015.
[50]
J. Andersson, E. Lindgren och H. Shahgholian, "Optimal regularity for the obstacle problem for the p-Laplacian," Journal of Differential Equations, vol. 259, no. 6, s. 2167-2179, 2015.
[51]
L. A. Caffarelli och H. Shahgholian, "Regularity of free boundaries a heuristic retro," Philosophical Transactions. Series A : Mathematical, physical, and engineering science, vol. 373, no. 2050, 2015.
[52]
A. Figalli och H. Shahgholian, "A General Class of Free Boundary Problems for Fully Nonlinear Elliptic Equations," Archive for Rational Mechanics and Analysis, vol. 213, no. 1, s. 269-286, 2014.
[53]
H. Aleksanyan, H. Shahgholian och P. Sjölin, "Applications of Fourier Analysis in Homogenization of Dirichlet Problem III : Polygonal Domains," Journal of Fourier Analysis and Applications, vol. 20, no. 3, s. 524-546, 2014.
[54]
H. Aleksanyan, H. Shahgholian och P. Sjölin, "Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates," Journal of Differential Equations, vol. 254, no. 6, s. 2626-2637, 2013.
[55]
H. Mikayelyan och H. Shahgholian, "Convexity Of The Free Boundary For An Exterior Free Boundary Problem Involving The Perimeter," Communications on Pure and Applied Analysis, vol. 12, no. 3, s. 1431-1443, 2013.
[56]
H. Shahgholian och T. Sjodin, "Harmonic balls and the two-phase Schwarz function," Complex Variables and Elliptic Equations, vol. 58, no. 6, s. 837-852, 2013.
[57]
J. Andersson, E. Lindgren och H. Shahgholian, "Optimal Regularity for the No-Sign Obstacle Problem," Communications on Pure and Applied Mathematics, vol. 66, no. 2, s. 245-262, 2013.
[58]
J. Andersson, E. Lindgren och H. Shahgholian, "Optimal regularity for the parabolic no-sign obstacle type problem," Interfaces and free boundaries (Print), vol. 15, no. 4, s. 477-499, 2013.
[59]
J. Andersson, H. Shah Gholian och G. S. Weiss, "The singular set of higher dimensional unstable obstacle type problems," Rendiconti Lincei - Matematica e Applicazioni, vol. 24, no. 1, s. 123-146, 2013.
[60]
H. Shahgholian, "Diversifications of Serrin's and related symmetry problems," Complex Variables and Elliptic Equations, vol. 57, no. 6, s. 653-665, 2012.
[61]
J. Andersson, H. Shahgholian och G. S. Weiss, "Double Obstacle Problems with Obstacles Given by Non-C-2 Hamilton-Jacobi Equations," Archive for Rational Mechanics and Analysis, vol. 206, no. 3, s. 779-819, 2012.
[62]
J. Andersson, H. Shahgholian och G. S. Weiss, "On the singularities of a free boundary through Fourier expansion," Inventiones Mathematicae, vol. 187, no. 3, s. 535-587, 2012.
[63]
B. Emamizadeh, J. V. Prajapat och H. Shahgholian, "A Two Phase Free Boundary Problem Related to Quadrature Domains," Potential Analysis, vol. 34, no. 2, s. 119-138, 2011.
[64]
H. Shahgholian och C. Babaoglu, "Symmetry in multi-phase overdetermined problems," Journal of Convex Analysis, vol. 18, s. 1013-1024, 2011.
[65]
J. Andersson, H. Shahgholian och G. S. Weiss, "Uniform Regularity Close to Cross Singularities in an Unstable Free Boundary Problem," Communications in Mathematical Physics, vol. 296, no. 1, s. 251-270, 2010.
[66]
T. Arnarson et al., "A PDE approach to regularity of solutions to finite horizon optimal switching problems," Nonlinear Analysis, vol. 71, no. 12, s. 6054-6067, 2009.
[67]
H. Shahgholian, N. Uraltseva och G. S. Weiss, "A parabolic two-phase obstacle-like equation," Advances in Mathematics, vol. 221, no. 3, s. 861-881, 2009.
[68]
E. Lindgren, H. Shahgholian och A. Edquist, "On the two-phase membrane problem with coefficients below the Lipschitz threshold," Annales de l'Institut Henri Poincare. Analyse non linéar, vol. 26, no. 6, s. 2359-2372, 2009.
[69]
H. Shahgholian, "Free boundary regularity close to initial state for parabolic obstacle problem," Transactions of the American Mathematical Society, vol. 360, no. 4, s. 2077-2087, 2008.
[70]
A. Petrosyan och H. Shahgholian, "Geometric and energetic criteria for the free boundary regularity in an obstacle-type problem," American Journal of Mathematics, vol. 129, no. 6, s. 1659-1688, 2007.
[71]
T. Kilpelaeinen, H. Shahgholian och X. Zhong, "Growth estimates through scaling for quasilinear partial differential equations," Annales Academiae Scientiarum Fennicae Mathematica, vol. 32, no. 2, s. 595-599, 2007.
[72]
H. Shahgholian och A. Petrosyan, "Parabolic obstacle problems applied to finance," Contemporary Mathematics, vol. 439, s. 117-133, 2007.
[73]
H. Shahgholian, N. Uraltseva och G. S. Weiss, "The Two-Phase Membrane Problem-Regularity of the Free Boundaries in Higher Dimensions," International mathematics research notices, 2007.
[74]
A. L. Karakhanyan, C. E. Kenig och H. Shahgholian, "The behavior of the free boundary near the fixed boundary for a minimization problem," Calculus of Variations and Partial Differential Equations, vol. 28, no. 1, s. 15-31, 2007.
[75]
H. Shahgholian, "The singular set for the composite membrane problem," Communications in Mathematical Physics, vol. 271, no. 1, s. 93-101, 2007.
[76]
A. Acker, M. Poghosyan och H. Shahgholian, "Convex configurations for solutions to semilinear elliptic problems in convex rings," Communications in Partial Differential Equations, vol. 31, no. 9, s. 1273-1287, 2006.
[77]
H. Shahgholian och G. S. Weiss, "The two-phase membrane problem - An intersection-comparison approach to the regularity at branch points," Advances in Mathematics, vol. 205, no. 2, s. 487-503, 2006.
[78]
H. Shahgholian, "When does the free boundary enter into corner points of the fixed boundary?," Journal of Mathematical Sciences, vol. 132, no. 3, s. 371-377, 2006.
[79]
B. Kawohl och H. Shahgholian, "Gamma limits in some Bernoulli free boundary problem," Archiv der Mathematik, vol. 84, no. 1, s. 79-87, 2005.
[80]
J. Andersson och H. Shahgholian, "Global solutions of the obstacle problem in half-spaces, and their impact on local stability," Calculus of Variations and Partial Differential Equations, vol. 23, no. 3, s. 271-279, 2005.
[81]
R. Monneau och H. Shahgholian, "Non-convexity of level sets in convex rings for semilinear elliptic problems," Indiana University Mathematics Journal, vol. 54, no. 2, s. 465-471, 2005.
[82]
A. Hakobyan och H. Shahgholian, "A uniqueness result for an overdetermined problem in non-linear parabolic potential theory," Potential Analysis, vol. 21, no. 4, s. 405-414, 2004.
[83]
L. Caffarelli, J. Salazar och H. Shahgholian, "Free-boundary regularity for a problem arising in superconductivity," Archive for Rational Mechanics and Analysis, vol. 171, no. 1, s. 115-128, 2004.
[84]
H. Shahgholian, N. Uraltseva och G. S. Weiss, "Global solutions of an obstacle-problem-like equation with two phases," Monatshefte für Mathematik (Print), vol. 142, no. 2-Jan, s. 27-34, 2004.
[85]
D. E. Apushkinskaya, N. N. Ural’Tseva och H. Shahgholian, "Lipschitz property of the free boundary in the parabolic obstacle problem," St. Petersburg Mathematical Journal, vol. 15, no. 3, s. 375-391, 2004.
[86]
L. Caffarelli, A. Petrosyan och H. Shahgholian, "Regularity of a free boundary in parabolic potential theory," Journal of The American Mathematical Society, vol. 17, no. 4, s. 827-869, 2004.
[87]
A. Acker et al., "The multi-layer free boundary problem for the p-Laplacian in convex domains," Interfaces and free boundaries (Print), vol. 6, no. 1, s. 81-103, 2004.
[88]
H. Shahgholian och L. A. Caffarelli, "The structure of the singular set of a free boundary in potential theory," Izv. Nats. Akad. Nauk Armenii Mat., vol. 39, no. 2, s. 43-58, 2004.
[89]
D. Danielli, A. Petrosyan och H. Shahgholian, "A singular perturbation problem for the p-Laplace operator," Indiana University Mathematics Journal, vol. 52, no. 2, s. 457-476, 2003.
[90]
H. Shahgholian, "Analysis of the free boundary for the p-parabolic variational problem (p >= 2)," Revista matemática iberoamericana, vol. 19, no. 3, s. 797-812, 2003.
[91]
I. Blank och H. Shahgholian, "Boundary Regularity and Compactness for Overdetermined Problems," Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, vol. 2, no. 4, s. 787-802, 2003.
[92]
H. Shahgholian, "C-1,C-1 regularity in semilinear elliptic problems," Communications on Pure and Applied Mathematics, vol. 56, no. 2, s. 278-281, 2003.
[93]
K. Lee och H. Shahgholian, "Hausdorff measure and stability for the p-obstacle problem (2 < p
[94]
H. Shahgholian och N. Uraltseva, "Regularity properties of a free boundary near contact points with the fixed boundary," Duke mathematical journal, vol. 116, no. 1, s. 1-34, 2003.
[95]
H. Shahgholian och N. Arakelian, "Uniform and tangential approximation on a strip by entire functions having optimal growth," Computational methods in Function Theory, vol. 3, no. 1-2, s. 359-383, 2003.
[96]
J. Manfredi, A. Petrosyan och H. Shahgholian, "A free boundary problem for infinity-Laplace equation," Calculus of Variations and Partial Differential Equations, vol. 14, no. 3, s. 359-384, 2002.
[97]
A. Henrot och H. Shahgholian, "The one phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition," Transactions of the American Mathematical Society, vol. 354, no. 6, s. 2399-2416, 2002.
[98]
K. A. Lee och H. Shahgholian, "Regularity of a free boundary for viscosity solutions of nonlinear elliptic equations," Communications on Pure and Applied Mathematics, vol. 54, no. 1, s. 43-56, 2001.
[99]
H. Shahgholian, "Dense subsets of L-1-solutions to linear elliptic partial differential equations," Journal of Approximation Theory, vol. 102, no. 2, s. 189-216, 2000.
[100]
A. Henrot och H. Shahgholian, "Existence of classical solutions to a free boundary problem for the p-Laplace operator : (II) The interior convex case," Indiana University Mathematics Journal, vol. 49, no. 1, s. 311-323, 2000.
[101]
A. Henrot och H. Shahgholian, "Existence of classical solutions to a free boundary problem for the p-Laplace operator : (I) the exterior convex case," Journal für die Reine und Angewandte Mathematik, vol. 521, s. 85-97, 2000.
[102]
L. Karp et al., "On the porosity of free boundaries in degenerate variational inequalities," Journal of Differential Equations, vol. 164, no. 1, s. 110-117, 2000.
[103]
L. Karp och H. Shahgholian, "Regularity of a free boundary at the infinity point," Communications in Partial Differential Equations, vol. 25, no. 12-Nov, s. 2055-2086, 2000.
[104]
L. A. Caffarelli, L. Karp och H. Shahgholian, "Regularity of a free boundary with application to the Pompeiu problem," Annals of Mathematics, vol. 151, no. 1, s. 269-292, 2000.
Konferensbidrag
[105]
H. Shahgholian och G. S. Weiss, "Aleksandrov and Kelvin reflection and the regularity of free boundaries," i Free Boundary Problems : Theory and Applications, 2007, s. 391-401.
[106]
H. Shahgholian, N. Uraltseva och G. S. Weiss, "Global solutions of an obstacle-problem-like equation with two phases," i Nonlinear Differential Equation Models, 2004, s. 27-34.
Kapitel i böcker
[107]
H. Shahgholian, "Recent Trends in Free Boundary Regularity," i GEOMETRY OF PDES AND RELATED PROBLEMS, Bianchini, C Henrot, A Magnanini, R red., : SPRINGER INTERNATIONAL PUBLISHING AG, 2018, s. 147-196.
Icke refereegranskade
Artiklar
[108]
G.-Q. Chen, H. Shahgholian och J.-L. Vazquez, "Free boundary problems : the forefront of current and future developments," Philosophical Transactions. Series A : Mathematical, physical, and engineering science, vol. 373, no. 2050, 2015.
Senaste synkning med DiVA:
2024-04-28 00:46:02