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.

Local Boundedness for Weak Solutions to some Quasilinear Elliptic Systems

Francesco Leonetti;Cristina Pignotti;
2021

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/159758
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