Michele Caselli

Research interests

My research focuses on Geometric Analysis and Elliptic PDEs. In particular: 

• The classical and fractional Allen-Cahn equation, and the interplay between phase transitions and minimal surfaces. 

• Nonlocal minimal surfaces in Riemannian manifolds and nonlocal approximation of classical minimal surfaces. 

• Regularity theory of elliptic PDEs and obstacle problems.

Keywords: geometric analysis,  elliptic PDEs,  calculus of variations,  geometric measure theory,  currents and varifolds,  fractional perimeter,  nonlocal minimal surfaces,  fractional Sobolev spaces,  stability and minimal cones,  fractional Laplacian on manifolds,  Caffarelli–Silvestre extension,  singular integral operators,  Gamma-convergence,  sphere-valued Sobolev maps,  vortex lines,  min-max methods,  phase transitions,  Ginzburg-Landau model,  Allen-Cahn equation,  obstacle problems,  free boundary problems.