Stable Solutions of Elliptic Partial Differential Equations: 1st Edition (Paperback) book cover

Stable Solutions of Elliptic Partial Differential Equations

1st Edition

By Louis Dupaigne

Chapman and Hall/CRC

335 pages

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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.

About the Author

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

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
SCIENCE / Mathematical Physics