Glasnik Matematicki, Vol. 41, No.2 (2006), 283-297.

ISOPERIMETRIC INEQUALITIES FOR AN ELECTROSTATIC PROBLEM

L. Boukrim and T. Mekkaoui

Université My Ismaïl. F. S. T. Errachidia, Département de Mathématiques, BP 509 Boutalamine Errachidia, Morocco
e-mail: boukrim05@yahoo.fr
e-mail: toufik_mekkaoui@yahoo.fr


Abstract.   We study the problem of the (p-)capacity cp of a multiconnected configuration Ω = (G \ E) \ ( Hi) when G and E have given potentials. Here Ω represents a nonhomogeneous medium and the Hi, which separate the different connected components of Ω, represent perfect conductors. By comparison with a similar configuration with spherical symmetry, we give isoperimetric inequalities for cp and the unknown potentials on Hi.

2000 Mathematics Subject Classification.   26D10, 35J65.

Key words and phrases.   Isoperimetric inequality, rearrangement, nonlinear elliptic PDE's.


Full text (PDF) (free access)

DOI: 10.3336/gm.41.2.11


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