44 citations · 226 across the 56 of their papers we have counts for
59 papers · 1 filter
Partial regularity of the gradient for subsolutions
Aram Hakobyan, Michael Poghosyan, Henrik Shahgholian
We prove that the gradient of any bounded subharmonic function is upper semi-continuous, provided that its super-level sets can be touched from the exterior by uniform $C^{1,\text{…
A minimization problem with free boundary and its application to inverse scattering problems
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.
Constraint maps with free boundaries: the obstacle case
Alessio Figalli, Sunghan Kim, Henrik Shahgholian
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part…
A Minimization Problem with Free Boundary for -Laplacian weakly coupled System
Morteza Fotouhi, Henrik Shahgholian
In this paper we consider a weakly coupled -Laplacian system of a Bernoulli type free boundary problem, through minimization of a corresponding functional. We prove various prop…
Almost minimizers to a transmission problem for -Laplacian
Sunghan Kim, Henrik Shahgholian
This paper concerns almost minimizers of the functional where and is a bounded domain of $\ma…
On positivity sets for Helmholtz solutions
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles.…