5 citations · 13 across the 13 of their papers we have counts for
14 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 $$ \int_Ω\left(|\nabla…
Free boundary regularity for almost minimizers of the parabolic Signorini problem
Seongmin Jeon, Arshak Petrosyan
In this paper, we study the regularity of the "regular" part of the free boundary for almost minimizers in the parabolic Signorini problem with zero thin obstacle. This work is a c…
Convexity for a parabolic fully nonlinear free boundary problem with singular term
Seongmin Jeon, Henrik Shahgholian
In this paper, we study a parabolic free boundary problem in an exterior domain $$\begin{cases} F(D^2u)-\partial_tu=u^aχ_{\{u>0\}}&\text{in }(\mathbb R^n\setminus K)\times(0,\infty…
Higher order boundary Harnack principles in Dini type domains
Seongmin Jeon, Stefano Vita
Aim of this paper is to provide higher order boundary Harnack principles [De Silva-Savin 15] for elliptic equations in divergence form under Dini type regularity assumptions on bou…
Convexity for free boundaries with singular term (nonlinear elliptic case)
Seongmin Jeon, Henrik Shahgholian
We consider a free boundary problem in an exterior domain \begin{cases}\begin{array}{cc} Lu=g(u) & \text{in }Ω\setminus K, \\ u=1 & \text{on }\partial K,\\ |\nabla u|=0 &\text{on }…
Regularity of almost minimizers for the parabolic thin obstacle problem
Seongmin Jeon, Arshak Petrosyan
In this paper, we study almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their -regularity for every , as…
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…
Symmetry for a fully nonlinear free boundary problem with highly singular term
Layan El Hajj, Seongmin Jeon, Henrik Shahgholian
In this paper we prove radial symmetry for solutions to a free boundary problem with a singular right hand side, in both elliptic and parabolic regime. More exactly, in the unit ba…
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…
Almost minimizers for the thin obstacle problem with variable coefficients
Seongmin Jeon, Arshak Petrosyan, Mariana Smit Vega Garcia
We study almost minimizers for the thin obstacle problem with variable Hölder continuous coefficients and zero thin obstacle and establish their regularity on the either…
Almost minimizers for the thin obstacle problem
Seongmin Jeon, Arshak Petrosyan
We consider Anzellotti-type almost minimizers for the thin obstacle (or Signorini) problem with zero thin obstacle and establish their regularity on the either side of th…
Almost minimizers for certain fractional variational problems
Seongmin Jeon, Arshak Petrosyan
In this paper we introduce a notion of almost minimizers for certain variational problems governed by the fractional Laplacian, with the help of the Caffarelli-Silvestre extension.…