Stable Solutions of Elliptic Partial Differential Equations

Louis Dupaigne

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English

Chapman & Hall/CRC
23 September 2019

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
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 453g
ISBN: 9780367382971
ISBN 10: 0367382970
Pages: 335
Publication Date: 23 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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