Nonlinear Elliptic Equations and Nonassociative Algebras - Couverture rigide

Nadirashvili, Nikolai; Tkachev, Vladimir; Vladut, Serge

Couverture rigide

ISBN 10 : 1470417103 ISBN 13 : 9781470417109

Editeur : American Mathematical Society, 2015

Synopsis

This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of ``Hessian equations'', depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four.

Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.

A propos du livre

À propos de l'auteur

Nikolai Nadirashvili, Aix-Marseille University, France.

Vladimir Tkachev, Linkoping University, Sweden.

Serge Vladut, Aix-Marseille University, France.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2015
• Langue: anglais
• ISBN 10: 1470417103
• ISBN 13: 9781470417109
• Reliure: Relié
• Nombre de pages: 240
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible