Keller-Osserman estimates for some quasilinear elliptic systems

TL;DR

This paper establishes Keller-Osserman type a priori estimates for certain quasilinear elliptic systems, including mixed systems, and analyzes solution behavior near singularities, despite the absence of a comparison principle.

Contribution

It introduces new Keller-Osserman estimates for quasilinear systems with absorption or mixed terms, and studies solution properties without relying on comparison principles.

Findings

Proved Keller-Osserman type a priori estimates for the systems.

Showed that solutions of mixed systems satisfy Harnack inequality.

Analyzed solution behavior near zero, including removability and sharpness of estimates.

Abstract

In this article we study quasilinear multipower systems of two equations of two types, in a domain $\Omega$ of R^{N} : with absorption terms, or mixed terms. Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type. Concerning the mixed system, we show that one of the solutions always satisfies Harnack inequality. In the case $\Omega$=B(0,1)\{0}, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results.