Stable Solutions of Elliptic Partial Differential Equations

Louis Dupaigne, Haim Brezis

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Hardback

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English

Chapman & Hall/CRC
15 March 2011

Differential calculus & equations

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.

By: Louis Dupaigne
Series edited by: Haim Brezis
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Volume: 143
Dimensions: Height: 254mm, Width: 178mm, Spine: 23mm
Weight: 612g
ISBN: 9781420066548
ISBN 10: 1420066544
Pages: 336
Publication Date: 15 March 2011
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Stable Solutions of Elliptic Partial Differential Equations

the author has put every effort into giving complete details of the computations. ... the self-contained one hundred-page long appendices provide a splendid resource for the reader. The material contained there has been chosen with particular good taste and constitutes in itself a valuable source of information. Remarks and further features ... are presented in an `exercise' format. I have found many of them suitably posed and reasonable to work at the level of the book. -Jose C. Sabina de Lis, Mathematical Reviews, 2012i