Michele Caselli

Research interests

My research focuses on Phase Transitions and Elliptic PDEs. In particular: 

• Codimension-two models for minimal surfaces, such as the Ginzburg-Landau model and sphere-valued  fractional harmonic maps.

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

• Global analysis and analysis on manifolds. 

• Regularity theory of elliptic PDEs and obstacle problems.

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