29 citations · 161 across the 22 of their papers we have counts for
27 papers
Triple Junctions in Multi-Phase Obstacle type Problems
Daniela De Silva, Ovidiu Savin, Henrik Shahgholian
We study the regularity of the free boundary for a multi-phase obstacle-type problem associated to quadrature domains, which arises from the minimization of the energy $$J(U,F):= \…
Viscosity and variational approaches in free boundary problems: A Volume in Honor of Sandro Salsa
Daniela De Silva, Fausto Ferrari
Free boundary problems (FBPs) are differential equations where the domain depends on the solution, with applications in diverse fields such as flame propagation, financial mathemat…
Two-phase problems: Perron solutions and regularity of the Neumann problem in convex cones
Thomas Beck, Daniela De Silva, Ovidiu Savin
We investigate a fully nonlinear two-phase free boundary problem with a Neumann boundary condition on the boundary of a general convex set with corners. We…
An energy model for harmonic functions with junctions
Daniela De Silva, Ovidiu Savin
We consider an energy model for harmonic graphs with junctions and study the regularity properties of minimizers and their free boundaries.
Almost minimizers for a sublinear system with free boundary
Daniela De Silva, Seongmin Jeon, Henrik Shahgholian
We study vector-valued almost minimizers of the energy functional $$\int_D\left(|\nabla\mathbf{u}|^2+\frac2{1+q}\left(λ_+(x)|\mathbf{u}^+|^{q+1}+λ_-(x)|\mathbf{u}^-|^{q+1}\right)\r…
Uniform density estimates and -convergence for the Alt-Phillips functional of negative powers
Daniela De Silva, Ovidiu Savin
We obtain density estimates for the free boundaries of minimizers of the Alt-Phillips functional involving negative power potentials $$\int_Ω\left(|\nabla u|^2 + u^{-γ} χ…
Controlling for multiple covariates
Mark Tygert
A fundamental problem in statistics is to compare the outcomes attained by members of subpopulations. This problem arises in the analysis of randomized controlled trials, in the an…
On the Boundary Harnack Principle in Holder domains
Daniela De Silva, Ovidiu Savin
We investigate the Boundary Harnack Principle in Hölder domains of exponent by the analytical method developed in our previous work "A short proof of Boundary Harnack Princip…
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…
Perron's solutions for two-phase free boundary problems with distributed sources
Daniela De Silva, Fausto Ferrari, Sandro Salsa
We use Perron method to construct a weak solution to a two-phase free boundary problem with right-hand-side. We thus extend the results of the pioneer work of Caffarelli for the ho…
Boundary Harnack estimates in slit domains and applications to thin free boundary problems
Daniela De Silva, Ovidiu Savin
We provide a higher order boundary Harnack inequality for harmonic functions in slit domains. As a corollary we obtain the regularity of the free boundary in the Signori…
A note on higher regularity boundary Harnack inequality
Daniela De Silva, Ovidiu Savin
We show that the quotient of two positive harmonic functions vanishing on the boundary of a domain is of class up to the boundary.
regularity of certain thin free boundaries
Daniela De Silva, Ovidiu Savin
We continue our study of the free boundary regularity in the thin one-phase problem and show that free boundaries are smooth.
A one-phase problem for the fractional Laplacian: regularity of flat free boundaries
Daniela De Silva, Ovidiu Savin, Yannick Sire
We consider a one-phase free boundary problem involving a fractional Laplacian , and we prove that ``flat free boundaries" are . We thus extend the known…
Two-phase problems with distributed source: regularity of the free boundary
D. De Silva, F. Ferrari, S. Salsa
We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with non-zero right hand side. We prove that Lipschitz or flat free bound…
Regularity of Lipschitz free boundaries for the thin one-phase problem
Daniela De Silva, Ovidiu Savin
We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional $$\label{E} E(u,Ω) = \int_Ω|\nabla u|^2 dX + \…
C^{2,α}$ regularity of flat free boundaries for the thin one-phase problem
Daniela De Silva, Ovidiu Savin
We prove regularity of sufficiently flat free boundaries, for the thin one-phase problem in which the free boundary occurs on a lower dimensional subspace. This problem a…
Regularity in a one-phase free boundary problem for the fractional Laplacian
Daniela De Silva, Jean-Michel Roquejoffre
For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are . We recover the regularity results of Caffarelli for visc…
A gradient bound for free boundary graphs
Daniela De Silva, David Jerison
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every ener…
Free boundary regularity for a problem with right hand side
Daniela De Silva
We consider a one-phase free boundary problem with variable coefficients and non-zero right hand side. We prove that flat free boundaries are using a different approach t…