3 citations · 4 across the 8 of their papers we have counts for
10 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 $$J(U,F):= \…
Existence theory for non-variational systems with free boundaries
Layan El Hajj, Seongmin Jeon, Henrik Shahgholian
We study the existence of solutions for systems of both elliptic and parabolic partial differential equations with potentially singular right-hand sides and free boundaries, posed…
Remarks on the fine structure of the free boundary (the no-sign obstacle problem)
Seongmin Jeon, Henrik Shahgholian
We present a number of results inspired by the approach developed in a recent work by A. Figalli and J. Serra on the fine structure of the obstacle problem, which turns out to be p…
The free boundary for a superlinear system
Daniela De Silva, Seongmin Jeon, Henrik Shahgholian
In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_Ω\left(|\nabla…
The free boundary for semilinear problems with highly oscillating singular terms
Mark Allen, Dennis Kriventsov, Henrik Shahgholian
We investigate general semilinear (obstacle-like) problems of the form , where has a singularity/jump at giving rise to a free boundary. Unlike many wor…
Regularity near the fixed boundary for transmission systems
Alessio Figalli, Somayeh Khademloo, Sunghan Kim +1
Given with , open, and , we study elliptic systems of the type $$ {\rm div} \big( ( A + (B- A)χ_D)\nabla u\big) =…
Convexity for a parabolic fully nonlinear free boundary problem with singular term
Seongmin Jeon, Henrik Shahgholian
In this paper, we study a parabolic free boundary problem in an exterior domain $$\begin{cases} F(D^2u)-\partial_tu=u^aχ_{\{u>0\}}&\text{in }(\mathbb R^n\setminus K)\times(0,\infty…
Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the -Laplacian
Masoud Bayrami, Morteza Fotouhi, Henrik Shahgholian
For a given constant and a bounded Lipschitz domain (), we establish that almost-minimizers of the functional $$ J(\mathbf{v}; D) = \int_D…
Constraint maps with free boundaries: the Bernoulli case
Alessio Figalli, André Guerra, Sunghan Kim +1
In this manuscript, we delve into the study of maps that minimize the Alt-Caffarelli energy functional u…
A weakly coupled system of -Laplace type in a heat conduction problem
Morteza Fotouhi, Mohammad Safdari, Henrik Shahgholian
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.