Access the full text.
Sign up today, get DeepDyve free for 14 days.
L. Hedberg (1981)
Spectral synthesis in sobolev spaces, and uniqueness of solutions of the Dirichlet problemActa Mathematica, 147
G. Buttazzo, G. Maso (1993)
An existence result for a class of shape optimization problemsArchive for Rational Mechanics and Analysis, 122
P. Bassanini, A. Elcrat (1997)
Elliptic Partial Differential Equations of Second Order
P. Tilli (2000)
On a constrained variational problem with an arbitrary number of free boundariesInterfaces and Free Boundaries, 2
A. Friedman, Y. Liu (1994)
A free boundary problem arising in magnetohydrodynamic systemAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 22
L. Caffarelli, D. Jerison, C. Kenig (2002)
Some new monotonicity theorems with applications to free boundary problemsAnnals of Mathematics, 155
J. Heinonen, T. Kilpeläinen, O. Martio (1993)
Nonlinear Potential Theory of Degenerate Elliptic Equations
J. Descloux (1991)
Stability of the solutions of the bidimensional magnetic shaping problem in absence of surface tensionEuropean Journal of Mechanics B-fluids, 10
H. Alt, L. Caffarelli, A. Friedman (1984)
Variational problems with two phases and their free boundariesTransactions of the American Mathematical Society, 282
N. Aguilera, H. Alt, L. Caffarelli (1986)
An optimization problem with volume constraintSiam Journal on Control and Optimization, 24
C. Morrey (1966)
Multiple Integrals in the Calculus of Variations
E. Giusti (1977)
Minimal surfaces and functions of bounded variation
Mohammed Hayouni (1999)
Lipschitz continuity of the state function in a shape optimization problem.Journal of Convex Analysis, 6
J. Descloux (1994)
A stability result for the magnetic shaping problemZeitschrift für angewandte Mathematik und Physik ZAMP, 45
L. Evans (1992)
Measure theory and fine properties of functions
H. Shahgholian, Björn Gustafsson (1995)
Existence and geometric properties of solutions of a free boundary problem in potential theory.Journal für die reine und angewandte Mathematik (Crelles Journal), 1996
H. Alt, L. Caffarelli (1981)
Existence and regularity for a minimum problem with free boundary.Journal für die reine und angewandte Mathematik (Crelles Journal), 1981
M. Crouzeix (1990)
Variational approach of a magnetic shaping problemEuropean Journal of Mechanics B-fluids, 10
Tanguy Briançon (2004)
Regularity of optimal shapes for the Dirichlet's energy with volume constraintESAIM: Control, Optimisation and Calculus of Variations, 10
Antoine Henrot, M. Pierre (1989)
Un problème inverse en formage des métaux liquidesMathematical Modelling and Numerical Analysis, 23
Mohammed Hayouni (2000)
Sur la minimisation de la première valeur propre du LaplacienComptes Rendus De L Academie Des Sciences Serie I-mathematique, 330
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.
Calculus of Variations and Partial Differential Equations – Springer Journals
Published: Jan 1, 2004
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.