On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions

Details On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions

2012-03-06

arxiv.org/abs/1203.1298v2

Mathematics

Analysis of PDEs

29 pages. Few inconsistencies and misprints corrected, two references added

Scientific paper

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.

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