Stable Solutions of Elliptic Partial Differential Equations

Louis Dupaigne

ISBN 10: 1420066544 / ISBN 13: 9781420066548

Editore: Taylor & Francis Group, 2011

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pp. 335 Index.

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Dati bibliografici

• Titolo: Stable Solutions of Elliptic Partial Differential Equations
• Editore: Taylor & Francis Group
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 1420066544
• ISBN 13: 9781420066548
• Rilegatura: Rilegato
• Condizione: New

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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