The material will be chosen from the following topics:
The obstacle problem:
Specific topics to be treated in this course are chosen from various applications in physics, biology, industry, finance, and others.
Mathematical tools:
Basic functional analysis,
Function spaces,
Green's formula and boundary value problems,
Second order elliptic partiella, differentialekvationer,
The projection theorem,
Existence results,
Stability,
The goal of the course is to learn how to solve certain problems related to free boundaries that appear in various applied sciences.
This will also give insight in how mathematics---and in particular partial differential equations---can be used to formulate problems in physics, mechanics, finance, biology, and industry,
After completing the course students should understand and be able to apply the theory of variational calculus and partial differential equations to study specific problems chosen from applications.
A Master degree including at least 30 university credits (hp) in in Mathematics. Standard courses in Analysis on advanced level.
Lecture Notes by the examiner and other articles.
If the course is discontinued, students may request to be examined during the following two academic years.
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examination consists homework assignments and oral presentation of a project.
Approved assignments and presentations.
