Volume 6, Issue 3
C1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions

Chen Yazhe

J. Part. Diff. Eq., 6 (1993), pp. 193-216.

Published online: 1993-06

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  • 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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@Article{JPDE-6-193, author = {}, title = {C1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions}, journal = {Journal of Partial Differential Equations}, year = {1993}, volume = {6}, number = {3}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5710.html} }
TY - JOUR T1 - C1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions JO - Journal of Partial Differential Equations VL - 3 SP - 193 EP - 216 PY - 1993 DA - 1993/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5710.html KW - AB - 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.
Chen Yazhe. (1970). C1,α Regularity of Viscosity Solutions of Fully Nonlinear Elliptic PDE Under Natural Structure Conditions. Journal of Partial Differential Equations. 6 (3). 193-216. doi:
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