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

Alberto Farina; Enrico Valdinoci

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 2, page 616-627
- ISSN: 1292-8119

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topFarina, Alberto, and Valdinoci, Enrico. "Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s." ESAIM: Control, Optimisation and Calculus of Variations 19.2 (2013): 616-627. <http://eudml.org/doc/272759>.

@article{Farina2013,

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.},

author = {Farina, Alberto, Valdinoci, Enrico},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {gradient bounds; P-function estimates; rigidity results; -function estimates},

language = {eng},

number = {2},

pages = {616-627},

publisher = {EDP-Sciences},

title = {Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s},

url = {http://eudml.org/doc/272759},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Farina, Alberto

AU - Valdinoci, Enrico

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 2

SP - 616

EP - 627

AB - 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.

LA - eng

KW - gradient bounds; P-function estimates; rigidity results; -function estimates

UR - http://eudml.org/doc/272759

ER -

## References

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