# A symmetry problem in the calculus of variations

Journal of the European Mathematical Society (2006)

- Volume: 008, Issue: 1, page 139-154
- ISSN: 1435-9855

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topCrasta, Graziano. "A symmetry problem in the calculus of variations." Journal of the European Mathematical Society 008.1 (2006): 139-154. <http://eudml.org/doc/277557>.

@article{Crasta2006,

abstract = {We consider the integral functional
$J(u)=\int _\Omega [f(|Du|)−u]dx$, $u\in W^\{1,1\}_0(\Omega )$, where $\Omega \subset \mathbb \{R\}^n$, $n\ge 2$, is a nonempty bounded connected open subset of $\mathbb \{R\}^n$ with smooth boundary, and $\mathbb \{R\}\ni s\mapsto f(|s|)$ is a convex, differentiable function. We prove that if $J$ admits a minimizer in $W^\{1,1\}_0(\Omega )$ depending only on the distance from the boundary of $\Omega $, then $\Omega $ must be a ball.},

author = {Crasta, Graziano},

journal = {Journal of the European Mathematical Society},

keywords = {minimizers of integral functionals; distance function; Euler equation; calculus of variations; distance function; symmetry of solutions},

language = {eng},

number = {1},

pages = {139-154},

publisher = {European Mathematical Society Publishing House},

title = {A symmetry problem in the calculus of variations},

url = {http://eudml.org/doc/277557},

volume = {008},

year = {2006},

}

TY - JOUR

AU - Crasta, Graziano

TI - A symmetry problem in the calculus of variations

JO - Journal of the European Mathematical Society

PY - 2006

PB - European Mathematical Society Publishing House

VL - 008

IS - 1

SP - 139

EP - 154

AB - We consider the integral functional
$J(u)=\int _\Omega [f(|Du|)−u]dx$, $u\in W^{1,1}_0(\Omega )$, where $\Omega \subset \mathbb {R}^n$, $n\ge 2$, is a nonempty bounded connected open subset of $\mathbb {R}^n$ with smooth boundary, and $\mathbb {R}\ni s\mapsto f(|s|)$ is a convex, differentiable function. We prove that if $J$ admits a minimizer in $W^{1,1}_0(\Omega )$ depending only on the distance from the boundary of $\Omega $, then $\Omega $ must be a ball.

LA - eng

KW - minimizers of integral functionals; distance function; Euler equation; calculus of variations; distance function; symmetry of solutions

UR - http://eudml.org/doc/277557

ER -

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