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Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s

Published online by Cambridge University Press:  14 March 2013

Alberto Farina  and
Enrico Valdinoci
Alberto Farina
Affiliation:
LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, Faculté des Sciences, 33 rue Saint-Leu, 80039 Amiens Cedex 1, France. [email protected]
Enrico Valdinoci
Affiliation:
Università degli Studi di Milano, Dipartimento di Matematica, via Cesare Saldini 50, 20133 Milano, Italy; [email protected]
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Abstract

We prove pointwise gradient bounds for entire solutions of pde’s of the form

     ℒu(x) = ψ(x, u(x), ∇u(x)),

where 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.

Keywords

Gradient boundsP-function estimatesrigidity results
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 616 - 627
Copyright
© EDP Sciences, SMAI, 2013

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