Geodesic
A symmetry problem in the calculus of variations
Journal of the European Mathematical Society, Tome 8 (2006) no. 1, pp. 139-154.

Voir la notice de l'article provenant de la source EMS Press

We consider a class of integral functionals defined in a Sobolev space of functions vanishing at the boundary of a nonempty bounded connected open n-dimensional set. We prove that, if the functional admits a minimizer depending only on the distance from the boundary, then that set must be a ball.
DOI : 10.4171/jems/41
Classification : 49-XX, 53-XX, 00-XX
Keywords: Minimizers of integral functionals, Distance function, Euler equation 
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     author = {Graziano Crasta},
     title = {A symmetry problem in the calculus of variations},
     journal = {Journal of the European Mathematical Society},
     pages = {139--154},
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     year = {2006},
     doi = {10.4171/jems/41},
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Graziano Crasta. A symmetry problem in the calculus of variations. Journal of the European Mathematical Society, Tome 8 (2006) no. 1, pp. 139-154. doi : 10.4171/jems/41. http://geodesic.mathdoc.fr/articles/10.4171/jems/41/

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