11-97 Alberto Farina, Enrico Valdinoci
Pointwise estimates and rigidity results for possibly singular and degenerate elliptic PDEs with general nonlinearities (192K, pdf) Jun 17, 11
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Abstract. We prove pointwise gradient bounds for entire solutions of PDEs of the form $$ {\mathcal{L}} u(x)=\psi(x,u(x), abla u(x)),$$ where ${\mathcal{L}}$ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J.~Serrin are also recovered as particular cases of our approach.

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