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Lipschitz continuity of state functions in some optimal shaping

Lipschitz continuity of state functions in some optimal shaping We prove local Lipschitz continuity of the solution to the state equation in two kinds of shape optimization problems with constraint on the volume: the minimal shaping for the Dirichlet energy, with no sign condition on the state function, and the minimal shaping for the first eigenvalue of the Laplacian. This is a main first step for proving regularity of the optimal shapes themselves. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calculus of Variations and Partial Differential Equations Springer Journals

Lipschitz continuity of state functions in some optimal shaping

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References (21)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer-Verlag Berlin/Heidelberg
Subject
Mathematics; Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics
ISSN
0944-2669
eISSN
1432-0835
DOI
10.1007/s00526-004-0286-5
Publisher site
See Article on Publisher Site

Abstract

We prove local Lipschitz continuity of the solution to the state equation in two kinds of shape optimization problems with constraint on the volume: the minimal shaping for the Dirichlet energy, with no sign condition on the state function, and the minimal shaping for the first eigenvalue of the Laplacian. This is a main first step for proving regularity of the optimal shapes themselves.

Journal

Calculus of Variations and Partial Differential EquationsSpringer Journals

Published: Jan 1, 2004

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