Volume 5, Issue 4
A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems

Chen Yazhe

DOI:

J. Part. Diff. Eq., 5 (1992), pp. 1-12.

Published online: 1992-05

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  • Abstract

We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions.

  • Keywords

Hölder estimate for the gradient viscosity solutions mollification approach obstacle problems

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@Article{JPDE-5-1, author = {}, title = {A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {4}, pages = {1--12}, abstract = { We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5748.html} }
TY - JOUR T1 - A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems JO - Journal of Partial Differential Equations VL - 4 SP - 1 EP - 12 PY - 1992 DA - 1992/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5748.html KW - Hölder estimate for the gradient KW - viscosity solutions KW - mollification approach KW - obstacle problems AB - We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions.
Chen Yazhe. (1970). A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems. Journal of Partial Differential Equations. 5 (4). 1-12. doi:
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