Maximum and comparison principles for degenerate elliptic systems and some applications

TL;DR

This paper investigates maximum and comparison principles for degenerate elliptic systems, providing explicit bounds for principal eigenvalues based on the domain's measure, with applications to related mathematical problems.

Contribution

It introduces detailed maximum and comparison principles for degenerate elliptic systems and derives explicit eigenvalue bounds related to the domain measure.

Findings

Established maximum and comparison principles for degenerate elliptic systems.

Derived explicit lower bounds for principal eigenvalues based on domain measure.

Applied theoretical results to specific problems involving degenerate elliptic operators.

Abstract

In this paper we develop a detailed study on maximum and comparison principles for a degenerate elliptic system. Explicit lower bounds for principal eigenvalues of this system in terms of the measure of $\Omega$ are also proved.