Local boundedness for weak solutions to some quasilinear elliptic systems

TL;DR

This paper establishes local boundedness of weak solutions to certain quasilinear elliptic systems by imposing conditions on off-diagonal coefficients, overcoming limitations posed by De Giorgi's counterexample.

Contribution

It introduces a novel condition on off-diagonal coefficients that ensures local boundedness of weak solutions in quasilinear elliptic systems.

Findings

Proved local boundedness under new coefficient support conditions

Overcame limitations of De Giorgi's counterexample

Extended understanding of solution regularity in elliptic systems

Abstract

We consider quasilinear elliptic systems in divergence form. In general, we cannot expect that weak solutions are locally bounded because of De Giorgi's counterexample. Here we assume a condition on the support of off-diagonal coefficients that "keeps away" the counterexample and allows us to prove local boundedness of weak solutions.