NOC:Sobolev Spaces and Partial Differential Equations

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. Kesavan

NPTEL Co-ordinating Institute : IMSc

NPTEL Lecture Count : 85

NPTEL Course Size : 6.1 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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