TY  - BOOK
AU  - Nadirashvili,Nikolai
AU  - Tkachev,Vladimir
AU  - Vladut,Serge
TI  - Nonlinear elliptic equations and nonassociative algebras
T2  - Mathematical surveys and monographs
SN  - 9781470417109 (acidfree paper)
U1  - 510MS 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Jordan algebras
KW  - Nonassociative rings
KW  - Elliptic differential equations
N1  - Includes bibliographical references (pages 223-233) and index; 1. Nonlinear elliptic equations--
2. Division algebras, exceptional lie groups, and calibrations--
3. Jordan algebras and the cartan isoparametric cubics--
4. Solutions from trialities--
5. Solutions from isoparametric forms--
6. Cubic minimal cones--
7. Singular solutions in calibrated geometries--
Bibliography--
Notation--
Index.


N2  - 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
ER  -