bernoulli problem
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Author(s):  
Guido De Philippis ◽  
Luca Spolaor ◽  
Bozhidar Velichkov

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.


2020 ◽  
Vol 13 (3) ◽  
pp. 741-764 ◽  
Author(s):  
Dario Mazzoleni ◽  
Susanna Terracini ◽  
Bozhidar Velichkov

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 472
Author(s):  
Antonio Greco

We consider the exterior as well as the interior free-boundary Bernoulli problem associated with the infinity-Laplacian under a non-autonomous boundary condition. Recall that the Bernoulli problem involves two domains: one is given, the other is unknown. Concerning the exterior problem we assume that the given domain has a positive reach, and prove an existence and uniqueness result together with an explicit representation of the solution. Concerning the interior problem, we obtain a similar result under the assumption that the complement of the given domain has a positive reach. In particular, for the interior problem we show that uniqueness holds in contrast to the usual problem associated to the Laplace operator.


2015 ◽  
Vol 22 (2) ◽  
pp. 131-146
Author(s):  
François Bouchon ◽  
Laurent Chupin
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