W<sup>2,p</sup><sub>loc</sub>(\Omega)\cap C<sup>1,α</sup>(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations

W<sup>2,p</sup><sub>loc</sub>(\Omega)\cap C<sup>1,α</sup>(\bar Ω) Viscosity Solutions of Neumann Problems for Fully Nonlinear Elliptic Equations

Year:    1995

Author:    Jiguang Bao

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 3 : pp. 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}.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1995-JPDE-5654

Journal of Partial Differential Equations, Vol. 8 (1995), Iss. 3 : pp. 219–232

Published online:    1995-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Viscosity solutions

Author Details

Jiguang Bao