Regularity of the free boundary for the two-phase Bernoulli problem-Reference-Cited by-同舟云学术

Regularity of the free boundary for the two-phase Bernoulli problem

Published:2021-02-23 Issue:2 Volume:225 Page:347-394
ISSN:0020-9910
Container-title:Inventiones mathematicae
language:en
Short-container-title:Invent. math.

Author:

De Philippis Guido,Spolaor Luca,Velichkov Bozhidar

Abstract

AbstractWe prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.

Funder

Università di Pisa

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00222-021-01031-7.pdf

Reference46 articles.

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2. Alt, H.W., Caffarelli, L.A., Friedman, A.: Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2), 431–461 (1984)

3. Andersson, J., Weiss, G.S.: A parabolic free boundary problem with Bernoulli type condition on the free boundary. J. Reine Angew. Math. 6727, 213–235 (2009)

4. Andersson, J., Shahgholian, H., Weiss, G.S.: A variational linearization technique in free boundary problems applied to a two-phase Bernoulli problem. Pers. Commun.

5. Athanasopoulos, I., Caffarelli, L.A.: Optimal regularity of lower dimensional obstacle problems. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov 310, 49–66 (2004)

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