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

Shenghong Li

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 = {Shenghong Li }, 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} }
TY - JOUR T1 - Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint AU - Shenghong Li JO - Journal of Partial Differential Equations VL - 4 SP - 313 EP - 334 PY - 1998 DA - 1998/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5573.html KW - Regularity and existence KW - gradient constraint KW - viscosity solution AB - 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.
Shenghong Li . (1998). Regularity of Solution for Fully Nonlinear Second Order Elliptic Equation with Gradient Constraint. Journal of Partial Differential Equations. 11 (4). 313-334. doi:
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