NPTEL : NOC:Sobolev Spaces and Partial Differential Equations (Mathematics)

Co-ordinators : Prof. Kesavan


Lecture 1 - Test Functions - Part 1

Lecture 2 - Test Functions - Part 2

Lecture 3 - Distributions

Lecture 4 - Examples - Part 1

Lecture 5 - Distribution Derivatives

Lecture 6 - More operations on distributions

Lecture 7 - Support of a distribution

Lecture 8 - Distributions with compact support; singular support - Part 1

Lecture 9 - Distributions with compact support; singular support - Part 2

Lecture 10 - Exercises - Part 1

Lecture 11 - Convolution of functions - Part 1

Lecture 12 - Convolution of functions - Part 2

Lecture 13 - Convolution of functions - Part 3

Lecture 14 - Convolution of distributions - Part 1

Lecture 15 - Convolution of distributions - Part 2

Lecture 16 - Convolution of distributions - Part 3

Lecture 17 - Exercises - Part 2

Lecture 18 - Fundamental solutions

Lecture 19 - The Fourier transform

Lecture 20 - The Schwarz space - Part 1

Lecture 21 - The Schwarz space - Part 2

Lecture 22 - Examples - Part 1

Lecture 23 - Fourier inversion formula

Lecture 24 - Tempered distributions

Lecture 25 - Exercises - Part 3

Lecture 26 - Sobolev spaces - Part 1

Lecture 27 - Sobolev spaces - Part 2

Lecture 28 - Sobolev spaces - Part 3

Lecture 29 - Approximation by smooth functions

Lecture 30 - Chain rule and applications - Part 1

Lecture 31 - Chain rule and applications - Part 2

Lecture 32 - Extension theorems - Part 1

Lecture 33 - Extension theorems - Part 2

Lecture 34 - Poincare's inequlity

Lecture 35 - Exercises - Part 4

Lecture 36 - Exercises - Part 5

Lecture 37 - Imbedding theorems

Lecture 38 - Imbedding theorems: Case p less than N - Part 1

Lecture 39 - Imbedding theorems: Case p = N - Part 2

Lecture 40 - Imbedding theorems: Case p greater than N - Part 3

Lecture 41 - Compactness theorems - Part 1

Lecture 42 - Compactness theorems - Part 2

Lecture 43 - Compactness theorems - Part 3

Lecture 44 - The spaces W^{s,p}

Lecture 45 - spaces W^{s,p} and Trace spaces

Lecture 46 - Trace theory - Part 1

Lecture 47 - Trace theory - Part 2

Lecture 48 - Trace theory - Part 3

Lecture 49 - Trace theory - Part 4

Lecture 50 - Exercises - Part 6

Lecture 51 - Exercises - Part 7

Lecture 52 - Abstract variational problems - Part 1

Lecture 53 - Abstract variational problems - Part 2

Lecture 54 - Weak solutions of elliptic boundary value problems - Part 1

Lecture 55 - Weak solutions of elliptic boundary value problems - Part 2

Lecture 56 - Neumann problems

Lecture 57 - The Biharmonic operator

Lecture 58 - The elasticity system

Lecture 59 - Exercises - Part 8

Lecture 60 - Exercises - Part 9

Lecture 61 - Exercises - Part 9

Lecture 62 - Maximum Principles - Part 1

Lecture 63 - Maximum Principles - Part 2

Lecture 64 - Exercises - Part 10

Lecture 65 - Exercises - Part 11

Lecture 66 - Eigenvalue problems - Part 1

Lecture 67 - Eigenvalue problems - Part 2

Lecture 68 - Eigenvalue problems - Part 3

Lecture 69 - Exercises - Part 12

Lecture 70 - Exercises - Part 13

Lecture 71 - Unbounded operators - Part 1

Lecture 72 - Unbounded operators - Part 2

Lecture 73 - The exponential map

Lecture 74 - C_0 Semigroups - Part 1

Lecture 75 - C_0 Semigroups - Part 2

Lecture 76 - Infinitesimal generators of contraction semigroups

Lecture 77 - Hille-Yosida theorem

Lecture 78 - Regularity

Lecture 79 - Contraction semigroups on Hilbert spaces

Lecture 80 - Self-adjoint case and the case of isometries

Lecture 81 - The heat equation

Lecture 82 - The wave equation

Lecture 83 - The Schrodinger equation

Lecture 84 - The inhomogeneous equation

Lecture 85 - Exercises - 14