Differential and Integral Equations

Hölder continuity in a shape-optimization problem with perimeter

Nicolas Landais

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations Volume 20, Number 6 (2007), 657-670.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039430

Mathematical Reviews number (MathSciNet)
MR2319460

Subjects
Primary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90]
Secondary: 35B65: Smoothness and regularity of solutions 35R35: Free boundary problems 49N60: Regularity of solutions

Citation

Landais, Nicolas. Hölder continuity in a shape-optimization problem with perimeter. Differential Integral Equations 20 (2007), no. 6, 657--670. https://projecteuclid.org/euclid.die/1356039430.


Export citation