Linear Elliptic Equations of Second Order
by Erich Miersemann
Publisher: Leipzig University 2012
Number of pages: 87
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.
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by A.D.R. Choudary, Saima Parveen, Constantin Varsan - arXiv
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects.
by K. Yosida - Tata Institute of Fundamental Research
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.
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A 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.
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The author develops the most basic ideas from the theory of partial differential equations, and apply them to the simplest models arising from physics. He presents some of the mathematics that can be used to describe the vibrating circular membrane.