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Zusatztext 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.-José C. Sabina de Lis! Mathematical Reviews! 2012i Informationen zum Autor Louis Dupaigne is an assistant professor at Université Picardie Jules Verne in Amiens, France. Klappentext This book offers a self-contained presentation of the notion of stability in 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 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 covers the inverse-square potential and submanifolds of Euclidean space. Zusammenfassung 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 and geometry. This book offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). Inhaltsverzeichnis 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.
