<em>C</em><sup>1,α</sup> Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions
Year: 1993
Journal of Partial Differential Equations, Vol. 6 (1993), Iss. 3 : pp. 193–216
Abstract
In this paper we are concemed with fully nonlinear elliptic equation F(x, u, Du, D²u) = 0. We establish the interior Lipschitz continuity and C^{1,α} regularity of viscosity solutions under natural structure conditions without differentiating the equation as usual, especially we give a new analytic Harnack inequality approach to C^{1,α} estimate for viscosity solutions instead of the geometric approach given by L. Caffarelli \& L. Wang and improve their results. Our structure conditions are rather mild.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1993-JPDE-5710
Journal of Partial Differential Equations, Vol. 6 (1993), Iss. 3 : pp. 193–216
Published online: 1993-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24