Lectures on Partial Differential Equations By G.B. Folland

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Lectures on Partial Differential Equations written by G.B. Folland, Indian Institute of Science, Bangalore, India.

Lectures on Partial Differential Equations written by G.B. Folland cover the following topics.

Preliminaries
General Theorems About Convolutions, The Fourier Transform, Some Results From the Theory of Distributions

Partial Differential Operators with Constant Coefficients
Local Solvability and Fundamental Solution, Regularity Properties of Differential Operators, Basic Operators in Mathematical Physics, Laplace Operator, The Heat Operator, The Wave Operator

L2 Sobolev Spaces
General Theory of L, Sobolev Spaces, Hypoelliptic Operators With Constant Coefficients

Basic Theory of Pseudo Differential Operators
Representation of Pseudo differential Operators, Distribution Kernels and the Pseudo Local Property, Asymptotic Expansions of Symbols, Properly Supported Operators, ψdo′s Defined by Multiple Symbols, Products and Adjoint of ψDO′S, A Continuity Theorem for ψ Do on Sobolev Spaces, Elliptic Pseudo Differential Operators, Wavefront Sets, Some Further Applications

LP and Lipschitz Estimates

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