Butterfly support for off diagonal coefficients and boundedness of solutions to quasilinear 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 that off-diagonal coefficients have a “butterfly support”: this allows us to prove local boundedness of weak solutions.

Keywords

• quasilinear
• elliptic
• system
• weak
• solution
• regularity
• primary: 35j47
• secondary: 35b65
• 49n60