# Some possibly degenerate elliptic problems with measure data and non linearity on the boundary

Thierry Gallouët^{[1]}; Yannick Sire^{[2]}

- [1] Université Aix-Marseille 1 – LATP – Marseille, France
- [2] Université Aix-Marseille 3, Paul Cézanne – LATP – Marseille, France

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

- Volume: 20, Issue: 2, page 231-245
- ISSN: 0240-2963

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topGallouët, Thierry, and Sire, Yannick. "Some possibly degenerate elliptic problems with measure data and non linearity on the boundary." Annales de la faculté des sciences de Toulouse Mathématiques 20.2 (2011): 231-245. <http://eudml.org/doc/219788>.

@article{Gallouët2011,

abstract = {The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a bounded domain with measure supported on the domain and on the boundary. A second one deals with the same type of data but involves a degenerate weight in the equation. In both cases, the nonlinearity under consideration lies on the boundary. For the first problem, we prove an optimal regularity result, whereas for the second one the optimality is not guaranteed but we provide however regularity estimates.},

affiliation = {Université Aix-Marseille 1 – LATP – Marseille, France; Université Aix-Marseille 3, Paul Cézanne – LATP – Marseille, France},

author = {Gallouët, Thierry, Sire, Yannick},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {Laplacian operator; degenerate elliptic equation; non-linear boundary conditions; mixed boundary conditions},

language = {eng},

month = {4},

number = {2},

pages = {231-245},

publisher = {Université Paul Sabatier, Toulouse},

title = {Some possibly degenerate elliptic problems with measure data and non linearity on the boundary},

url = {http://eudml.org/doc/219788},

volume = {20},

year = {2011},

}

TY - JOUR

AU - Gallouët, Thierry

AU - Sire, Yannick

TI - Some possibly degenerate elliptic problems with measure data and non linearity on the boundary

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2011/4//

PB - Université Paul Sabatier, Toulouse

VL - 20

IS - 2

SP - 231

EP - 245

AB - The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a bounded domain with measure supported on the domain and on the boundary. A second one deals with the same type of data but involves a degenerate weight in the equation. In both cases, the nonlinearity under consideration lies on the boundary. For the first problem, we prove an optimal regularity result, whereas for the second one the optimality is not guaranteed but we provide however regularity estimates.

LA - eng

KW - Laplacian operator; degenerate elliptic equation; non-linear boundary conditions; mixed boundary conditions

UR - http://eudml.org/doc/219788

ER -

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