A generalized Montel theorem for a class of first order elliptic equations with measurable coefficients

TL;DR

This paper generalizes Montel's theorem to certain elliptic equations with measurable coefficients, establishing precompactness of solution sequences and advancing the understanding of elliptic PDEs with less regular coefficients.

Contribution

It extends Montel's theorem to first order elliptic equations with measurable coefficients involving Hodge-Dirac operators and applies this to second order elliptic equations.

Findings

Established a generalized Montel theorem for elliptic equations with measurable coefficients.

Proved precompactness of solution sequences for second order elliptic equations.

Enhanced understanding of elliptic PDEs with irregular coefficients.

Abstract

In this paper we prove a generalization of Montel's theorem for a class of first order elliptic equations with measurable coefficients involving Hodge-Dirac operators. We then apply this result to sequences of solutions of second order uniformly elliptic equations with measurable coefficients on divergence form and show that this results in a precompactness result for such sequences.