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

Alberto Farina; Enrico Valdinoci

doi:10.1051/cocv/2012024

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

Alberto Farina, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We prove pointwise gradient bounds for entire solutions of pde's of the form u(x) = ψ(x, u(x), u(x)), where â"' 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.

Original language	English
Pages (from-to)	616-627
Number of pages	12
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	19
Issue number	2
DOIs	https://doi.org/10.1051/cocv/2012024
Publication status	Published - 1 Apr 2013
Externally published	Yes

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10.1051/cocv/2012024

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title = "Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's",

abstract = "We prove pointwise gradient bounds for entire solutions of pde's of the form u(x) = ψ(x, u(x), u(x)), where {\^a}{"}' 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 bounds, P-function estimates, Rigidity results",

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T1 - Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's

AU - Farina, Alberto

AU - Valdinoci, Enrico

PY - 2013/4/1

Y1 - 2013/4/1

N2 - We prove pointwise gradient bounds for entire solutions of pde's of the form u(x) = ψ(x, u(x), u(x)), where â"' 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.

AB - We prove pointwise gradient bounds for entire solutions of pde's of the form u(x) = ψ(x, u(x), u(x)), where â"' 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.

KW - Gradient bounds

KW - P-function estimates

KW - Rigidity results

UR - http://www.scopus.com/inward/record.url?scp=84876573845&partnerID=8YFLogxK

U2 - 10.1051/cocv/2012024

DO - 10.1051/cocv/2012024

M3 - Article

AN - SCOPUS:84876573845

SN - 1292-8119

VL - 19

SP - 616

EP - 627

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

IS - 2

ER -

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

Abstract

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