arXiv subjects

D. De Silva

Publications and source records attributed to D. De Silva.

6 recordsLinked to original sources

arXiv2016

The two membranes problem for different operators

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 solution approach to this problem. Then we obtain $C^{1,γ}$ regularity of the solutions provided that the orders of the two operators are different. In the special case when one operator coincides with the fractional Laplacian, we obtain the optimal regularity and a characterization of the free boundary.

math.AP↗

arXiv2016

Obstacle type problems for minimal surfaces

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.

math.AP↗

arXiv2013

Free boundary regularity for fully nonlinear non-homogeneous two-phase problems

We prove that flat or Lipschitz free boundaries of two-phase free boundary problems governed by fully nonlinear uniformly elliptic operators and with non-zero right hand side are $C^{1,γ}$.

math.AP↗

arXiv2012

Two-phase problems with distributed source: regularity of the free boundary

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 boundaries are $C^{1,γ}$. In particular, viscosity solutions are indeed classical.

math.AP↗

arXiv2007

Rearrangements and radial graphs of constant mean curvature in hyperbolic space

We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results are proved via rearrangement techniques.

math.AP↗

arXiv2007

Symmetry of global solutions to a class of fully nonlinear elliptic equations in 2D

We prove that entire bounded monotone solutions to a certain class of fully nonlinear equations in 2D are one-dimensional. Our result also gives a new (non-variational) proof of the well known De Giorgi's conjecture.

math.AP↗