Minimax Theory and its Applications 06 (2021), No. 2, 365--378
Copyright Heldermann Verlag 2021
Local Boundedness for Weak Solutions to some Quasilinear Elliptic Systems
Salvatore Leonardi
Dept. of Mathematics and Informatics, University of Catania, 95125 Catania, Italy
leonardi@dmi.unict.it
Francesco Leonetti
DISIM, University of L'Aquila, 67100 L'Aquila, Italy
leonetti@univaq.it
Cristina Pignotti
DISIM, University of L'Aquila, 67100 L'Aquila, Italy
pignotti@univaq.it
Eugenio Rocha
CIDMA, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
eugenio@ua.pt
Vasile Staicu
CIDMA, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
vasile@ua.pt
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.
Keywords: Quasilinear, elliptic, system, weak, solution, regularity.
MSC: 35J47; 35B65, 49N60.
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