# Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 4, page 559-575
- ISSN: 1292-8119

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topNazaret, Bruno. "Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 559-575. <http://eudml.org/doc/197335>.

@article{Nazaret2010,

abstract = {
This article is devoted to the study of a perturbation with a viscosity term
in an elliptic equation involving the p-Laplacian operator and related to
the best contant problem in Sobolev inequalities in the critical case.
We prove first that this problem, together with the equation, is stable
under this perturbation, assuming some conditions on the datas. In the
next section, we show that the zero solution is strongly isolated in some
sense, among the space of the solutions. Actually, we end the paper by
giving some analoguous results in the case where the datas present
symmetries.
},

author = {Nazaret, Bruno},

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

keywords = {Variational problems; nonlinear elliptic PDE; optimal Sobolev
inequalities; best constant problems; p-Laplacian operator.; perturbation; viscosity term; best constant problem in Sobolev inequalities},

language = {eng},

month = {3},

pages = {559-575},

publisher = {EDP Sciences},

title = {Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth},

url = {http://eudml.org/doc/197335},

volume = {4},

year = {2010},

}

TY - JOUR

AU - Nazaret, Bruno

TI - Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 4

SP - 559

EP - 575

AB -
This article is devoted to the study of a perturbation with a viscosity term
in an elliptic equation involving the p-Laplacian operator and related to
the best contant problem in Sobolev inequalities in the critical case.
We prove first that this problem, together with the equation, is stable
under this perturbation, assuming some conditions on the datas. In the
next section, we show that the zero solution is strongly isolated in some
sense, among the space of the solutions. Actually, we end the paper by
giving some analoguous results in the case where the datas present
symmetries.

LA - eng

KW - Variational problems; nonlinear elliptic PDE; optimal Sobolev
inequalities; best constant problems; p-Laplacian operator.; perturbation; viscosity term; best constant problem in Sobolev inequalities

UR - http://eudml.org/doc/197335

ER -

## References

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