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${W}^{2,p}$ Estimates for Elliptic Equations on $C^{1,α}$ Domains (2201.01975v1)
Published 6 Jan 2022 in math.AP
Abstract: 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 $C{1,\alpha}$ domains are obtained for nondivergence form linear elliptic equations and further more, fully nonlinear elliptic equations are also considered.
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