Interior Lp-estimates for elliptic and parabolic Schr\"odinger type operators and local Ap-weights

TL;DR

This paper establishes interior Lp-estimates for elliptic and parabolic Schrödinger operators with VMO coefficients and potentials satisfying reverse-Hölder conditions, using local A-weighted Sobolev spaces.

Contribution

It provides new a priori interior estimates for these operators in weighted Sobolev spaces with local A-weights, extending previous results to more general settings.

Findings

Derived interior Lp-estimates for elliptic Schrödinger operators.

Extended estimates to parabolic Schrödinger operators.

Incorporated local A-weights and boundary distance in the analysis.

Abstract

Let Omega be a non-empty open proper and connected subset of R^n. Consider p elliptic Schr\"odinger type operator L_{E}u=A_{E}u+V in Omega, and the linear parabolic operator L_{P}u=A_{P}u+Vu in Omega x (0,T), where the coefficients of A_{E} and A_{P} are in VMO and the potential V satisfies a reverse-H\"older condition. The aim of this paper is to obtain a priori estimates for the operators L_{E} and L_{P} in weighted Sobolev spaces involving the distance to the boundary and weights in a local-A class.