3 citations · 4 across the 8 of their papers we have counts for
9 papers
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…