Stable Solutions of Elliptic Partial Differential Equations

Louis Dupaigne

ISBN 10: 0367382970 / ISBN 13: 9780367382971

Published by Taylor & Francis Ltd, 2019

About this Item

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Bibliographic Details

• Title: Stable Solutions of Elliptic Partial Differential Equations
• Publisher: Taylor & Francis Ltd
• Publication Date: 2019
• Language: English
• ISBN 10: 0367382970
• ISBN 13: 9780367382971
• Binding: Paperback / softback
• Condition: New
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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.

About the Author

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