Regularity of the free boundary in an optimization problem related to the best sobolev trace constant

In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion $H^1(\Omega)\hookrightarrow L^q(\partial\Omega)$ for functions that vanish in a subset of $\Omega$. This problem is also related to a minimizati...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2005-01, Vol.44 (5), p.1614-1635
Main Authors: FERNANDEZ BONDER, Julian, ROSSI, Julio D, WOLANSKI, Noemi
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control theory. Systems
Eigenvalues
Exact sciences and technology
Mathematical programming
Miscellaneous
Operational research and scientific management
Operational research. Management science
Optimization
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Summary:In this paper we study the regularity properties of a free boundary problem arising in the optimization of the best Sobolev trace constant in the immersion $H^1(\Omega)\hookrightarrow L^q(\partial\Omega)$ for functions that vanish in a subset of $\Omega$. This problem is also related to a minimization problem for Steklov eigenvalues.
ISSN:0363-0129
1095-7138
DOI:10.1137/040613615