Interior W2,p(x)-regularity for elliptic equations of nondivergence form

Abstract

In this paper, we consider the following elliptic equations of nondivergence form∑i,j=1naij∂2u∂xi∂xj=f,in Ω⊂Rn, where the coefficients aij are real valued bounded measurable functions defined in Ω⊂Rn, belong to VMOloc (see Definition 2.5) and satisfy the uniformly elliptic condition. Under the assumption that p(⋅) satisfies the log-Hölder continuity condition, we will establish the interior W2,p(x)-regularity for strong solutions to the elliptic equations of nondivergence form.