Interior Lp-estimates for elliptic and parabolic Schrödinger type operators and local Ap-weights

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Let Omega be a non-empty open proper and connected subset of Rⁿ. Consider p elliptic Schrödinger type operator Lₑu=Aₑu+V in Omega, and the linear parabolic operator Lₚu=Aₚu+Vu in Omega x (0,T), where the coefficients of Aₑ and Aₚ are in VMO and the potential V satisfies a reverse-Hölder condition. The aim of this paper is to obtain a priori estimates for the operators Lₑ and Lₚ in weighted Sobolev spaces involving the distance to the boundary and weights in a local-A class.