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:
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Basic functional analysis,
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Function spaces,
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Green's formula and boundary value problems,
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Second order elliptic partiella, differentialekvationer,
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The projection theorem,
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Existence results,
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Stability,
- Comparison and maximum principles.
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.