Volume 11, Issue 4
Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint

Shenghong Li

DOI:

J. Part. Diff. Eq., 11 (1998), pp. 313-334.

Published online: 1998-11

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  • Abstract

The existence and regularity of the solution for the fully nonlinear second order elliptic equation with gradient constraint are discussed in this paper. We prove the existence of the strong solution by choice of special penalty function, and obtain the local W^{2,∞} estimate of the solution by means of the theory of viscosity solution with the auxiliary function method.

  • Keywords

Regularity and existence gradient constraint viscosity solution

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@Article{JPDE-11-313, author = {}, title = {Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {4}, pages = {313--334}, abstract = { The existence and regularity of the solution for the fully nonlinear second order elliptic equation with gradient constraint are discussed in this paper. We prove the existence of the strong solution by choice of special penalty function, and obtain the local W^{2,∞} estimate of the solution by means of the theory of viscosity solution with the auxiliary function method.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5573.html} }
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