Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic ... - 9781470447403

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic EquationsAuthor(s): N.V. Krylov\nFormat: Hardback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470447403, 978-1470447403\nSynopsis\nThis book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov-Safonov and the Evans-Krylov theorems, are taken from old sources, and the main results were obtained in the last few years.\n\nPresentation of these results is based on a generalization of the Fefferman-Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called ``ersatz'' existence theorems, saying that one can slightly modify ``any'' equation and get a ``cut-o.