Volume 4, Issue 1
Existence of Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations

Bian Baojun

J. Part. Diff. Eq.,4(1991),pp.21-32

Published online: 1991-04

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  • Abstract
We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D²u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^{1,∞} under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex.
  • Keywords

Viscosity solutions Second order fully nonlinear elliptic equations Existence

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@Article{JPDE-4-21, author = {Bian Baojun}, title = {Existence of Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {1}, pages = {21--32}, abstract = { We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D²u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^{1,∞} under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5758.html} }
TY - JOUR T1 - Existence of Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations AU - Bian Baojun JO - Journal of Partial Differential Equations VL - 1 SP - 21 EP - 32 PY - 1991 DA - 1991/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5758.html KW - Viscosity solutions KW - Second order fully nonlinear elliptic equations KW - Existence AB - We consider the problem of existence for viscosity solutions of seoond order fully nonlinear elliptic partial differential equations F(D²u, Du, u, z) = 0. We prove existence results for viscosity solutions in W^{1,∞} under assumptions that function F satisfies the natural structure conditions. We do not assume F is convex.
Bian Baojun. (1970). Existence of Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations. Journal of Partial Differential Equations. 4 (1). 21-32. doi:
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