Credits: 3 (3-0-0)
Description
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.
Prerequisite Tree
flowchart TD
MTL792-1048[MTL792]
MTL792-1048 --- Or1049[Any one of]:::empty
MTL104-1050 --> MTL101-1050[MTL101]
MTL411-1050 --> MTL122-1050[MTL122]
MTL411-1050 --> MTL104-1050[MTL104]
Or1049 -.-> MTL411-1050[MTL411]
MTL122-1050 --> MTL100-1050[MTL100]
Or1049 -.-> MTL602-1051[MTL602]
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