Nonlinear Analysis and Differential Equations
Additional Info
- ECTS credits: 6
- University: University of Granada
- Semester: 3
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Topics:
1 Sobolev Spaces:
Weak derivatives, duality of Sobolev spaces.Weak topology in Sobolev spaces.Sobolev inequalities and the Rellich theorem.
2 Eigenvalues and Eigenfunctions of the Laplacian:
Analysis of spectral properties associated with the Laplace operator.
3 Differential Calculus in Banach Spaces:
Fundamental concepts and applications of calculus within the framework of Banach spaces.
4 Implicit Function Theorem and Bifurcation Theory in Banach Spaces:
Examination of the implicit function theorem and its implications for bifurcation phenomena in higher-dimensional spaces.
5 Overdetermined Elliptic Problems:
Study of elliptic partial differential equations with an excess of boundary conditions.
6 Moving Plane Method and Symmetry Results:
Application of the moving plane method to obtain symmetry properties of solutions to differential equations.
