4 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(|\nabl…
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…