Stable Solutions of Elliptic Partial Differential Equations  book cover
1st Edition

Stable Solutions of Elliptic Partial Differential Equations

ISBN 9781420066548
Published March 15, 2011 by Chapman and Hall/CRC
335 Pages

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Book Description

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces).

Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.

Table of Contents

Defining Stability. The Gelfand Problem. Extremal Solutions. Regularity Theory of Stable Solutions. Singular Stable Solutions. Liouville Theorems for Stable Solutions. A Conjecture of E De Giorgi. Further Readings. Appendices. References. Index.

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Louis Dupaigne is an assistant professor at Université Picardie Jules Verne in Amiens, France.

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Author - Louis  Dupaigne

Louis Dupaigne

Maitre de conférences, Université Picardie Jules Verne

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