My general research interests are in calculus of variations and
geometric measure theory (CVGMT) and spectral theory (ST). More precisely:
existence and regularity in CVGMT:
free boundary problems (with or without elastic energy)
including boundary discontinuities such as partitions, internal cracks,
wetting, edge delaminations, debonding, brittle fractures;
(anisotropic and crystalline) minimal surfaces;
capillarity problems; area functional;
higher order problems related to perimeter (such as Willmore problem);
evolution in CVGMT:
geometric evolution problems
such as (anisotropic and crystalline) mean curvature flow, mean
curvature flow of partitions; quasitatic evolution problems of
elastic materials; nonlocal evolution problems;
discrete Schrodinger operators in ST:
coupling constant threshold phenomenon;
multiparticle lattice systems, location of essential spectrum,
existence of discrete spectrum, Efimov effect; asymptotics of
eigenvalues.