Stable Solutions of Elliptic Partial Differential Equations
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.
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.
Louis Dupaigne is an assistant professor at Université Picardie Jules Verne in Amiens, France.
Date de parution : 09-2019
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 14 jours).
Prix indicatif 74,82 €
Ajouter au panierDate de parution : 05-2011
Ouvrage de 306 p.
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 208,65 €
Ajouter au panierThèmes de Stable Solutions of Elliptic Partial Differential Equations :
Mots-clés :
Morse Index; Boundary Point Lemma; morse; Stable Solutions; index; Strong Maximum Principle; strong; Elliptic Regularity; maximum; Standard Elliptic Regularity; principle; Extremal Solution; bifurcation; Stable Branch; diagram; Compact Set; unit; Fractional Laplacian; ball; Euclidean Space RN; hardy's; Bifurcation Diagrams; Weak Solution; Liouville Type Theorem; Sobolev Inequality; Nondecreasing Convex Function; Standard Elliptic Estimates; Minimal Solution; Principal Eigenvalue; Banach Space; Energy Functional; Asymptotically Stable; U2 Dσ; Mountain Pass Solution; Monotone Solution