44 citations · 226 across the 56 of their papers we have counts for
63 papers
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{…
Teaching Mathematics and Sustainability (A narration of a rough journey)
Henrik Shahgholian
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic…
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…