${W}^{2,p}$ Estimates for Elliptic Equations on $C^{1,α}$ Domains

In this paper, a new method is represented to investigate boundary $W^{2,p}$ estimates for elliptic equations, which is, roughly speaking, to derive boundary $W^{2,p}$ estimates from interior $W^{2,p}$ estimates by Whitney decomposition. Using it, $W^{2,p}$ estimates on $C^{1,α}$ domains are obtained for nondivergence form linear elliptic equations and further more, fully nonlinear elliptic equations are also considered.

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