19 papers
Rectifiability of free boundaries in singular diffusion problems
Rafayel Teymurazyan
For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is -rectifiable. The argument relies on a suitable integra…
Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces
Giuseppe Di Fazio, Rafayel Teymurazyan, José Miguel Urbano
We establish sharp local -regularity for weak solutions to degenerate elliptic equations of -Laplacian type with data in Morrey spaces. The proof relies on the Fefferma…
Improved regularity for a nonlocal dead-core problem
Disson dos Prazeres, Rafayel Teymurazyan, José Miguel Urbano
We obtain improved regularity results for solutions to a nonlocal dead-core problem at branching points. Our approach, which does not rely on the maximum principle, introduces a ne…
Interacting free boundaries in obstacle problems
Damião J. Araújo, Rafayel Teymurazyan
We study obstacle problems governed by two distinct types of diffusion operators involving interacting free boundaries. We obtain a somewhat surprising coupling property, leading t…
Geometric properties of free boundaries in degenerate quenching problems
Damião J. Araújo, Rafayel Teymurazyan, José Miguel Urbano
We study minimizers of non-differentiable functionals modeled on the degenerate quenching problem. Our main result establishes the finiteness of the dimensional Hausdorff m…
The fractional Laplacian: a primer
Rafayel Teymurazyan
In this note we give a glimpse of the fractional Laplacian. In particular, we bring several definitions of this non-local operator and series of proofs of its properties. It is str…
Sharp regularity for singular obstacle problems
Damião J. Araújo, Rafayel Teymurazyan, Vardan Voskanyan
We obtain sharp local regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by …
An optimal Liouville theorem for the porous medium equation
Damião J. Araújo, Rafayel Teymurazyan
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the he…
Fully nonlinear dead-core systems
Damião J. Araújo, Rafayel Teymurazyan
We study fully nonlinear dead-core systems coupled with strong absorption terms. We discover a chain reaction, exploiting properties of an equation along the system and obtain high…
Reaction-diffusion equations for the infinity Laplacian
Nicolau M. L. Diehl, Rafayel Teymurazyan
We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side does not change sign and satisfi…
Non-local diffusion with free boundaries
Diego Marcon, Rafayel Teymurazyan
We prove optimal regularity and derive several geometric properties for solutions of a free boundary problem with fractional diffusion. Additionally, we deduce local regu…
Fully nonlinear integro-differential equations with deforming kernels
Luis Caffarelli, Rafayel Teymurazyan, José Miguel Urbano
We develop a regularity theory for integro-differential equations with kernels deforming in space like sections of a convex solution of a Monge-Ampère equation. We prove an ABP est…
Homogenization of obstacle problems in Orlicz-Sobolev spaces
Diego Marcon, José Francisco Rodrigues, Rafayel Teymurazyan
We study the homogenization of obstacle problems in Orlicz-Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the -Laplacian type.…
Sharp regularity estimates for quasilinear evolution equations
Marcelo D. Amaral, João Vítor da Silva, Gleydson C. Ricarte +1
We establish sharp geometric regularity estimates for bounded weak solutions of evolution equations of -Laplacian type. Our approach is based on geometric tangential m…
A free boundary optimization problem for the -Laplacian
Rafayel Teymurazyan, José Miguel Urbano
We study a free boundary optimization problem in heat conduction, ruled by the infinity-Laplace operator, with lower temperature bound and a volume constraint. We obtain existence…
Cavity type problems ruled by infinity Laplacian operator
Gleydson Chaves Ricarte, João Vítor da Silva, Rafayel Teymurazyan
We study a singularly perturbed problem related to infinity Laplacian operator with prescribed boundary values in a region. We prove that solutions are locally (uniformly) Lipschit…
Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries
Gleydson C. Ricarte, Rafayel Teymurazyan, José Miguel Urbano
We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder continuous in time…
Optimal design problems with fractional diffusions
Eduardo V. Teixeira, Rafayel Teymurazyan
In this article we study optimization problems ruled by -fractional diffusion operators with volume constraints. By means of penalization techniques we prove existence of soluti…
On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications
J. F. Rodrigues, R. Teymurazyan
We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic op…