Nonlinear Elliptic Equations and Nonassociative Algebras

Nonlinear Elliptic Equations and Nonassociative Algebras
Author :
Publisher : American Mathematical Soc.
Total Pages : 250
Release :
ISBN-10 : 9781470417109
ISBN-13 : 1470417103
Rating : 4/5 (103 Downloads)

Book Synopsis Nonlinear Elliptic Equations and Nonassociative Algebras by : Nikolai Nadirashvili

Download or read book Nonlinear Elliptic Equations and Nonassociative Algebras written by Nikolai Nadirashvili and published by American Mathematical Soc.. This book was released on 2014-12-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Nonlinear Elliptic Equations and Nonassociative Algebras Related Books

Nonlinear Elliptic Equations and Nonassociative Algebras
Language: en
Pages: 250
Authors: Nikolai Nadirashvili
Categories: Mathematics
Type: BOOK - Published: 2014-12-03 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear e
Elliptic Regularity Theory by Approximation Methods
Language: en
Pages: 203
Authors: Edgard A. Pimentel
Categories: Mathematics
Type: BOOK - Published: 2022-09-29 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.
Associative and Non-Associative Algebras and Applications
Language: en
Pages: 338
Authors: Mercedes Siles Molina
Categories: Mathematics
Type: BOOK - Published: 2020-01-02 - Publisher: Springer Nature

DOWNLOAD EBOOK

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Moro
Integro-Differential Elliptic Equations
Language: en
Pages: 409
Authors: Xavier Fernández-Real
Categories: Differential equations, Elliptic
Type: BOOK - Published: 2024 - Publisher: Springer Nature

DOWNLOAD EBOOK

Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in t
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs
Language: en
Pages: 148
Authors: Emanuel Indrei
Categories: Mathematics
Type: BOOK - Published: 2023-01-09 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February