Stable Solutions of Elliptic Partial Differential Equations

ISBN-13: 9781420066548 / Angielski / Twarda / 2011 / 335 str.

Lous Dupaigne

Opis

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). The author makes unique use of the Gelfand problem as a unifying theme and utilizes stability as a central tool. He also presents many other classical techniques, such as phase plane analysis, fixed point arguments, and blow-up analysis, and modern approaches, such as concave truncation, perturbation, and computer-assisted proofs, to study elliptic differential equations.

Spis treści

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.

O autorze

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