Existence, multiplicity, perturbation, and concentration results for a class of quasi-linear elliptic problems
by Marco Squassina
Publisher: Electronic Journal of Differential Equations 2006
Number of pages: 213
The aim of this monograph is to present a comprehensive survey of results about existence, multiplicity, perturbation from symmetry and concentration phenomena for a class of quasi-linear elliptic equations coming from functionals of the calculus of variations which turn out to be merely continuous. Some tools of non-smooth critical point theory will be employed.
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by Erich Miersemann - Leipzig University
These lecture notes are intended as an introduction to linear second order elliptic partial differential equations. From the table of contents: Potential theory; Perron's method; Maximum principles; A discrete maximum principle.
by Lawrence C. Evans - UC Berkeley
This course surveys various uses of 'entropy' concepts in the study of PDE, both linear and nonlinear. This is a mathematics course, the main concern is PDE and how various notions involving entropy have influenced our understanding of PDE.
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The purpose of this course was to introduce students to the applications of Fourier analysis -- by which I mean the study of convolution operators as well as the Fourier transform itself -- to partial differential equations.
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In these lectures, we shall be concerned with the differentiability and the representation of one-parameter semi-groups of bounded linear operators on a Banach space and their applications to the initial value problem for differential equations.