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2007 Hölder continuity in a shape-optimization problem with perimeter
Nicolas Landais
Differential Integral Equations 20(6): 657-670 (2007).

Abstract

Here, we prove Hölder continuity of the state function in a shape-optimization problem arising, for instance, in the electromagnetic shaping of a liquid metal. The equilibrium state is obtained as minimizing the total energy, which is given in the form $$ \mathcal{E}_\lambda(\Omega) = J(\Omega) + P(\Omega) + \lambda ||\Omega| - m| , $$ where $\Omega$ is the domain occupied by the liquid, $P(\Omega)$ and $|\Omega|$ being respectively the perimeter and the Lebesgue measure of $\Omega$. We prove that the state function associated with the optimal shape is $\frac{1}{2}$-H\"older continuous, the main difficulty coming from the fact that the state function is not assumed to be non-negative.

Citation

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Nicolas Landais. "Hölder continuity in a shape-optimization problem with perimeter." Differential Integral Equations 20 (6) 657 - 670, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35512
MathSciNet: MR2319460

Subjects:
Primary: 49Q10
Secondary: 35B65, 35R35, 49N60

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 6 • 2007
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