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

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,α domains are obtained for nondivergence form linear elliptic equations and further more, fully nonlinear elliptic equations are also considered.

Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries

“…The Liouville theorem on cones can be deduced with the aid of the boundary pointwise regularity (see [13]). The boundary pointwise regularity has been employed in the establishment of the global W 2,p regularity on a C 1,α domain for an appropriate 0 < α < 1 (see [11]).…”