Մաթեմատիկայի և մեխանիկայի ֆակուլտետ
Faculty of Mathematics and Mechanics
Training of specialists-mathematicians started in the YSU in 1924, in the physical - mathematical subsection of Social Science Department which became Physical-mathematical Department in 1993.:
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Henrik Sh. Shahgholian

Professor | Chair of General Mathematics
Positions
Jan 2001-current: Full Professor of Mathematics, KTH The Royal Institute of Technology, Stockholm, Sweden,
1998-2001: Associate Professor, KTH
1991-1998: Lecturer, KTH
1987-1991: Doctoral student, KTH

Research
Free boundary problems, partial diff. eq., potential theory, Numerical PDE, Applied and industrial problems, Mathematical Finance, Homogenization

Honors/Awards/Grants
Awarded honorary doctorate from Yerevan State University, April 2021.
Swedish Institute grant for visit to Armenia Fall 2019.
Swedish Research Council 2018-2021 (grants since 1993; with two years missing)
STINT grant: collaboration with Jiao Tong Shanghai, 3 years, finishes 2019
Knut and Alice Wallenberg Fund (postdocs Hayk Aleksanyan 2016-2017, Sunghan Kim 2020-2021)
STINT grant: collaboration with Seoul National Univ. 3 years, finished 2015
Qatar National research Fund 2012—2016
Simons visiting professor MSRI, Spring 2011
Elected foreign member of National Armenian Academy of Sciences 2008
Letterstedtska Prize from Royal Swedish Academy of Sciences, for Brilliant Mathematics of 2008

Current research work
I am currently working on various problems related to free boundaries. These include symmetry and rigidity properties for solutions to PDEs, where we aim at proving that certain solutions to partial differential equations with overdetermined boundary values have to have specific shapes, such as being a spheres, or half-planes, ellipsoids etc. Such problems are of wide interested in PDEs, and there are several problems untouched in the area. Our prime goal is remove previous assumptions, such as smoothness or apriori geometric restrictions.

A second topic I have been involved with, and plan to work on are the consideration of free boundaries for system of equations. These problems are in general extremely hard, due to lack of tools present in the scalar case. Here we need to develop new tools to treat such problems. The system case of free boundaries, usually offer no a priori regularity,and one may even encounter examples with singularities. As such we need to find correct assumptions, to circumvent such examples, and difficulties.

A third problem I work on is the so-called non scattering phenomena in inverse scattering theory. This problem deals with object hidden inside other objects and the question is how to detect them. A method of approach is to use waves for detection. The question that arise is what type of objects can be detected by such wave-indices. A regularity theory may tell us that certain objects with without corners may not be detected. So our study concerns the regularity of such objects given certain data for studying such objects.

Publications
Total of 115 publications in peer reviewed international journals. 3 Books and chapters

Languages
Armenian (native), Swedish, English, Persian (full professional efficiency)

E-mail
henriksh@math.kth.se

Henrik Shahgholian , Georg S. Weiss, Fotouhi Morteza
A free boundary problem for an elliptic system
2021 | Article
J. Differential Equations 284 (2021), 126–155.
Henrik Shahgholian , Dennis Kriventsov
Optimal regularity for a two-phase obstaclelike problem with logarithmic singularity
2021 | Article
Comm. Partial Differential Equations 46, (2021), no. 10, 1831–1850.
Free boundary methods and non-scattering phenomena
2021 | Article
Res. Math. Sci. 8 (2021), no. 4, Paper No. 58, 19 pp.
Henrik Shahgholian , El Hajj Layan
Radial symmetry for an elliptic PDE with a free boundary
2021 | Article
Proc. Amer. Math. Soc. Ser. B 8 (2021), 311–319.
Henrik Shahgholian , Marius Ghergu, Kim Sunghan
Isolated singularities for semilinear elliptic systems with power-law nonlinearity
2020 | Article
Anal. PDE 13 (2020), no. 3, 701
Henrik Shahgholian , Fotouhi Morteza, Andreas Minne, Georg S. Weiss
Remarks on the decay/growth rate of solutions to elliptic free boundary problems of obstacle type
2020 | Article
Math. Eng. 2 (2020), no. 4, 698–708.
Henrik Shahgholian , Hayk Aleksanyan
Perturbed divisible sandpiles and quadrature surfaces
2019 | Book
Potential Anal. 51 (2019), no. 4, 511–540.