TY - JOUR
T1 - 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
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 &gt; 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}.