MTL792
| MTL792 | |
|---|---|
| Modern Methods in Partial Differential equations | |
| Credits | 3 |
| Structure | 3-0-0 |
| Pre-requisites | MTL411/MTL602 |
| Overlaps | |
MTL792 : Modern Methods in Partial Differential equations
[edit]Review of Lebesgue integration and Classical function spaces, Spaces of infinitely differentiable functions and Holder spaces. Sobolev spaces: L^p spaces, Weak derivatives, Sobolev spaces, approximation to identity, approximation with smooth functions, trace spaces, Sobolev and Poincare inequalities, compact embeddings and negative order Sobolev spaces. Second order elliptic equations: Weak solutions, Lax-Milgram Theorem, Energy estimates, Fredlhom-alternative, Regularity of weak solutions, Maximum principles and eigenvalue problems. Mountain Pass lemma and applications. Hardy's inequalities and their relation with Elliptic equations. Linear Evolution equations: Second order parabolic equations, existence and regularity of weak solutions, Maximum principles. Semi-group Theory: Generating, contraction semi-groups and applications.