Nonlinear Partial Differential Equations of Elliptic Type
by Vicentiu Radulescu
Publisher: arXiv 2005
Number of pages: 114
The goal of this textbook is to provide the background which is necessary to initiate work on a Ph.D. thesis in Applied Nonlinear Analysis. The purpose is to provide for the student a broad perspective in the subject, to illustrate the rich variety of phenomena encompassed by it and to impart a working knowledge of the most important techniques of analysis of the solutions of the equations.
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by Richard S. Laugesen - arXiv
This text aims at highlights of spectral theory for self-adjoint partial differential operators, with an emphasis on problems with discrete spectrum. The course aims to develop your mental map of spectral theory in partial differential equations.
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Contents: Preliminaries; Local Existence Theory; Fourier Series; One-dimensional Heat Equation; One-dimensional Wave Equation; Laplace Equation; Laplace Operator; Dirichlet and Neumann Problems; Layer Potentials; The Heat Operator; The Wave Operator.
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