Prashantt492: Creating course page via bot

2026-03-04T10:15:02Z

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{{Infobox Course
| code = MTL792
| name = Modern Methods in Partial Differential equations
| credits = 3
| credit_structure = 3-0-0
| pre_requisites = MTL411/MTL602
| overlaps =
}}

== MTL792 : Modern Methods in Partial Differential equations ==
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.

MTL792 - Revision history

Prashantt492: Creating course page via bot