Learn · Sobolev Spaces and Partial Differential Equations
Lecture 43 of 85Week 7
Compactness theorems - Part 3
Prof. S. Kesavan · IMSc
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- Sobolev Spaces and Partial Differential Equations, IMSc (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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All the lectures
- Test Functions - Part 1
- Test Functions - Part 2
- Distributions
- Examples - Part 1
- Distribution Derivatives
- More operations on distributions
- Support of a distribution
- Distributions with compact support; singular support - Part 1
- Distributions with compact support; singular support - Part 2
- Exercises - Part 1
- Convolution of functions - Part 1
- Convolution of functions - Part 2
- Convolution of functions - Part 3
- Convolution of distributions - Part 1
- Convolution of distributions - Part 2
- Convolution of distributions - Part 3
- Exercises - Part 2
- Fundamental solutions
- The Fourier transform
- The Schwarz space - Part 1
- The Schwarz space - Part 2
- Examples - Part 1
- Fourier inversion formula
- Tempered distributions
- Exercises - Part 3
- Sobolev spaces - Part 1
- Sobolev spaces - Part 2
- Sobolev spaces - Part 3
- Approximation by smooth functions
- Chain rule and applications - Part 1
- Chain rule and applications - Part 2
- Extension theorems - Part 1
- Extension theorems - Part 2
- Poincare's inequlity
- Exercises - Part 4
- Exercises - Part 5
- Imbedding theorems
- Imbedding theorems: Case p < N - Part 1
- Imbedding theorems:Case p = N - Part 2
- Imbedding theorems: Case p > N - Part 3
- Compactness theorems - Part 1
- Compactness theorems - Part 2
- Compactness theorems - Part 3
- The spaces W^{s,p}
- Spaces W^{s,p} and Trace spaces
- Trace theory - Part 1
- Trace theory - Part 2
- Trace theory - Part 3
- Trace theory - Part 4
- Exercises - Part 6
- Exercises - Part 7
- Abstract variational problems - Part 1
- Abstract variational problems - Part 2
- Weak solutions of elliptic boundary value problems - Part 1
- Weak solutions of elliptic boundary value problems - Part 2
- Neumann problems
- The Biharmonic operator
- The elasticity system
- Exercises - Part 8
- Exercises - Part 9
- The Galerkin method
- Maximum Principles - Part 1
- Maximum Principles - Part 2
- Exercises - Part 10
- Exercises - Part 11
- Eigenvalue problems - Part 1
- Eigenvalue problems - Part 2
- Eigenvalue problems - Part 3
- Exercises - Part 12
- Exercises - Part 13
- Unbounded operators - Part 1
- Unbounded operators - Part 2
- The exponential map
- C_0 Semigroups - Part 1
- C_0 Semigroups - Part 2
- Infinitesimal generators of contraction semigroups
- Hille-Yosida theorem
- Regularity
- Contraction semigroups on Hilbert spaces
- Self-adjoint case and the case of isometries
- The heat equation
- The wave equation
- The Schrodinger equation
- The inhomogeneous equation
- Exercises - 14