Sobolev Spaces and Partial Differential Equations MEERCJ18BB

URI	`m2://res/MEERCJ18BB`
Kind	course
Creators	S. Kesavan (instructor)
Date	2021-06-08
MSC	35-XX
Scope	in

Expressions

e1: edition

Language	en
Date	2021-06-08

m1: page, IMSc (record). nptel 111106154
m2: page, 2021-06-08 (record). nptel 111106154

Contents

part 1: Week 1
session 1: Test Functions - Part 1
session 2: Test Functions - Part 2
session 3: Distributions
session 4: Examples - Part 1
session 5: Distribution Derivatives
session 6: More operations on distributions
session 7: Support of a distribution
part 2: Week 2
session 8: Distributions with compact support; singular support - Part 1
session 9: Distributions with compact support; singular support - Part 2
session 10: Exercises - Part 1
session 11: Convolution of functions - Part 1
session 12: Convolution of functions - Part 2
session 13: Convolution of functions - Part 3
session 14: Convolution of distributions - Part 1
part 3: Week 3
session 15: Convolution of distributions - Part 2
session 16: Convolution of distributions - Part 3
session 17: Exercises - Part 2
session 18: Fundamental solutions
session 19: The Fourier transform
session 20: The Schwarz space - Part 1
session 21: The Schwarz space - Part 2
part 4: Week 4
session 22: Examples - Part 1
session 23: Fourier inversion formula
session 24: Tempered distributions
session 25: Exercises - Part 3
session 26: Sobolev spaces - Part 1
session 27: Sobolev spaces - Part 2
session 28: Sobolev spaces - Part 3
part 5: Week 5
session 29: Approximation by smooth functions
session 30: Chain rule and applications - Part 1
session 31: Chain rule and applications - Part 2
session 32: Extension theorems - Part 1
session 33: Extension theorems - Part 2
session 34: Poincare's inequlity
part 6: Week 6
session 35: Exercises - Part 4
session 36: Exercises - Part 5
session 37: Imbedding theorems
session 38: Imbedding theorems: Case p < N - Part 1
session 39: Imbedding theorems:Case p = N - Part 2
session 40: Imbedding theorems: Case p > N - Part 3
session 41: Compactness theorems - Part 1
part 7: Week 7
session 42: Compactness theorems - Part 2
session 43: Compactness theorems - Part 3
session 44: The spaces W^{s,p}
session 45: Spaces W^{s,p} and Trace spaces
session 46: Trace theory - Part 1
session 47: Trace theory - Part 2
part 8: Week 8
session 48: Trace theory - Part 3
session 49: Trace theory - Part 4
session 50: Exercises - Part 6
session 51: Exercises - Part 7
session 52: Abstract variational problems - Part 1
session 53: Abstract variational problems - Part 2
session 54: Weak solutions of elliptic boundary value problems - Part 1
part 9: Week 9
session 55: Weak solutions of elliptic boundary value problems - Part 2
session 56: Neumann problems
session 57: The Biharmonic operator
session 58: The elasticity system
session 59: Exercises - Part 8
session 60: Exercises - Part 9
session 61: The Galerkin method
part 10: Week 10
session 62: Maximum Principles - Part 1
session 63: Maximum Principles - Part 2
session 64: Exercises - Part 10
session 65: Exercises - Part 11
session 66: Eigenvalue problems - Part 1
session 67: Eigenvalue problems - Part 2
session 68: Eigenvalue problems - Part 3
session 69: Exercises - Part 12
part 11: Week 11
session 70: Exercises - Part 13
session 71: Unbounded operators - Part 1
session 72: Unbounded operators - Part 2
session 73: The exponential map
session 74: C_0 Semigroups - Part 1
session 75: C_0 Semigroups - Part 2
session 76: Infinitesimal generators of contraction semigroups
session 77: Hille-Yosida theorem
part 12: Week 12
session 78: Regularity
session 79: Contraction semigroups on Hilbert spaces
session 80: Self-adjoint case and the case of isometries
session 81: The heat equation
session 82: The wave equation
session 83: The Schrodinger equation
session 84: The inhomogeneous equation
session 85: Exercises - 14

Catalogue records

nptel: 111106154 (manifestation)
nptel_video: 111106154 (manifestation)