Volume 19, Number 2, April-June 2013
|Page(s)||616 - 627|
|Published online||14 March 2013|
Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s
LAMFA, CNRS UMR 6140, Université de Picardie Jules Verne, Faculté
des Sciences, 33 rue
Amiens Cedex 1,
2 Università degli Studi di Milano, Dipartimento di Matematica, via Cesare Saldini 50, 20133 Milano, Italy
Received: 21 December 2011
Revised: 19 June 2012
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.
Mathematics Subject Classification: 35J60 / 35B45
Key words: Gradient bounds / P-function estimates / rigidity results
© EDP Sciences, SMAI, 2013
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