On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions
Analysis of PDEs
2012-04-03 v2
Abstract
We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second derivatives locally bounded solution in a given smooth domain with smooth boundary data. The approximating equation is constructed in such a way that it modifies the original one only for large values of the unknown function and its derivatives.
Keywords
Cite
@article{arxiv.1203.1298,
title = {On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions},
author = {N. V. Krylov},
journal= {arXiv preprint arXiv:1203.1298},
year = {2012}
}
Comments
29 pages. Few inconsistencies and misprints corrected, two references added