902 citations
- Columbia UniversityUS332 papers
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12 papers · 1 filter
Segregated configurations involving the square root of the laplacian and their free boundaries
Daniela De Silva, Susanna Terracini
We study the local structure and the regularity of free boundaries of segregated critical configurations involving the square root of the laplacian. We develop an improvement of fl…
Regularity of higher order in two-phase free boundary problems
Daniela De Silva, Fausto Ferrari, Sandro Salsa
We develop further the strategy implemented in our series of papers on inhomogeneous two-phase fee boundary problems, to show that flat or Lipschitz free boundaries of such problem…
Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D
Luis Caffarelli, Daniela De Silva, Ovidiu Savin
We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we ob…
Obstacle type problems for minimal surfaces
L. Caffarelli, D. De Silva, O. Savin
We study certain obstacle type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.
The two membranes problem for different operators
L. Caffarelli, D. De Silva, O. Savin
We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the Hölder continuity of the solutions and we develop a viscosity sol…
Regularity of the free boundary for two-phase problems governed by divergence form equations and applications
Daniela De Silva, Fausto Ferrari, Sandro Salsa
We study a class of two-phase inhomogeneous free boundary problems governed by elliptic equations in divergence form. In particular we prove that Lipschitz or flat free boundaries…