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Volume 8, Issue 3
W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations

Jiguang Bao

J. Part. Diff. Eq., 8 (1995), pp. 219-232.

Published online: 1995-08

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  • Abstract
In this paper we study fully nonlinear elliptic equations F(D²u, x) = 0 in Ω ⊂ R^n with Neumann boundary conditions \frac{∂u}{∂v} = a(x)u under the rather mild structure conditions and without the concavity condition. We establish the global C^{1,Ω} estimates and the interior W^{2,p} estimates for W^{2,q}(Ω) solutions (q > 2n) by introducing new independent variables, and moreover prove the existence of W^{2,p}_{loc}(Ω)∩ C^{1,α}(\bar \Omega} viscosity solutions by using the accretive operator methods, where p E (0, 2), α ∈ (0, 1}.
  • Keywords

Viscosity solutions Neumann boundary conditions fully nonlinear equations global C^{1 α} estimates interior W^{2 p} estimates

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@Article{JPDE-8-219, author = {Bao , Jiguang}, title = {W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {3}, pages = {219--232}, abstract = { In this paper we study fully nonlinear elliptic equations F(D²u, x) = 0 in Ω ⊂ R^n with Neumann boundary conditions \frac{∂u}{∂v} = a(x)u under the rather mild structure conditions and without the concavity condition. We establish the global C^{1,Ω} estimates and the interior W^{2,p} estimates for W^{2,q}(Ω) solutions (q > 2n) by introducing new independent variables, and moreover prove the existence of W^{2,p}_{loc}(Ω)∩ C^{1,α}(\bar \Omega} viscosity solutions by using the accretive operator methods, where p E (0, 2), α ∈ (0, 1}.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5654.html} }
TY - JOUR T1 - W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations AU - Bao , Jiguang JO - Journal of Partial Differential Equations VL - 3 SP - 219 EP - 232 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5654.html KW - Viscosity solutions KW - Neumann boundary conditions KW - fully nonlinear equations KW - global C^{1 KW - α} estimates KW - interior W^{2 KW - p} estimates AB - In this paper we study fully nonlinear elliptic equations F(D²u, x) = 0 in Ω ⊂ R^n with Neumann boundary conditions \frac{∂u}{∂v} = a(x)u under the rather mild structure conditions and without the concavity condition. We establish the global C^{1,Ω} estimates and the interior W^{2,p} estimates for W^{2,q}(Ω) solutions (q > 2n) by introducing new independent variables, and moreover prove the existence of W^{2,p}_{loc}(Ω)∩ C^{1,α}(\bar \Omega} viscosity solutions by using the accretive operator methods, where p E (0, 2), α ∈ (0, 1}.
Jiguang Bao . (2019). W2,ploc(\Omega)\cap C1,α(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations. Journal of Partial Differential Equations. 8 (3). 219-232. doi:
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