Titlebook: Semilinear Elliptic Equations for Beginners; Existence Results vi Marino Badiale,Enrico Serra Textbook 2011 Springer-Verlag London Limited

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0172-5939 es.Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field978-0-85729-226-1978-0-85729-227-8Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Minimization Techniques: Compact Problems,ethods of constrained minimization, where one restricts the functional to a subset of functions on which it is bounded from below, and tries to establish the existence of a minimum point. Special care must then be employed to show that the constrained minimum is truly a critical point of the unconstrained functional.

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Introduction to Minimax Methods, contrary, we concentrate on the search of critical points that are not global minima, for example saddle points. The procedures to do this, called minimax methods, are quite elaborate, and we introduce the main steps gradually.

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0172-5939 it ideal for self-study.For each method of proof a prototypSemilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reach

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Introduction and Basic Results,istence results..In particular we present a review of differential calculus for functionals, with many examples, and we introduce the fundamental notion of weak solution that allows one to interpret solutions of elliptic problems as critical points of functionals..Convex functionals and their main p

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Minimization Techniques: Lack of Compactness,ut in the simplest case, it is manifest through the fact that minimizing sequences are maybe bounded, but not (pre-)compact in the function spaces where the problem is set..The reasons for this often come from geometrical or physical aspects, for instance when the problem is set on an unbounded doma