Course No
M478
Credit
4
Approval
Syllabus
Distribution Theory, Sobolev Spaces, Embedding theorems, Trace theorem. Dirichlet, Neumann and Oblique derivative problem, Weak formulation, Lax–Milgram, Maximum Principles– Weak and Strong Maximum Principles, Hopf Maximum Principle, Alexandroff-Bakelmann-Pucci Estimate.
Reference Books
- L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics 19, American Mathematical Society, 2010.
- H. Brezis, “Functional Analysis, Sobolev Spaces and Partial Differential Equations”, Universitext, Springer, 2011.
- R. A. Adams, J. J. F. Fournier, “Sobolev Spces”, Pure and Applied Mathematics 140, Elsevier/Academic Press, 2003.
- S. Kesavan, “Topics in Functional Analysis and Applications”, John Wiley & Sons, 1989.
- M. Renardy, R. C. Rogers, “An Introduction to Partial Differential Equations”, Springer, 2008.