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My research concerns mostly free boundary value problems: regularity and geometric aspects. Currently, I am trying ot apply my methods to my new interest, Financial Mathematics. Besides these directions, I am interested in applications of PDE in sciences in general, as well as in industrial problems.

Topics treated in my papers
Free boundary regularity
This topic is one that I have spent most time on, and it concerns in general the regularity of free boundaries that arise in different type of applications. The common point in all of these problems are that the governing equations are those of obstacle problem type:
Delta u = f(x,u,Du), where the function f has a jump discontinuity, but it is bounded:
The obstacle problem f = \chi_{u>0}
Two phase membrane f = \Lambda_+\chi_{u>0} - \lambda_- \chi_{u<0}
Convexity and Star-likeness
Global solutions
Composite membrane problem

Henrik Shahgholian's home page

Updated on 26 January, 2007.