Keywords:
Regularity theory; elliptic PDEs; p-Laplace operator; free boundary; Sobolev maps; shape optimization; anisotropic mean curvature flow; anisotropic fractional perimeters; isoperimetric problem with double density; Wulff shape; weak optimal transport; inverse problems
My research is in the area of calculus of variations, partial differential equations and geometric measure theory. I investigate the regularity and qualitative properties for free boundary type problems with a high codimensional free boundary set. I study how the topology of a Riemannian manifold affects minimizers of p-energy functionals defined on Sobolev spaces of manifold-valued functions. I work on shape identification problems. I search and establish PDE formulations for weak optimal transport problems. I work on anisotropic variational problems.
