Special Session 75: Recent developments in Nonlinear PDEs, non-uniformly elliptic problems and related topics

Regularity properties in obstacle-type problems for higher-order fractional powers of the Laplacian

Donatella Danielli
Arizona State University
USA
Co-Author(s):    Alaa Haj Ali, Arshak Petrosyan
Abstract:
In this talk we will discuss a sampler of obstacle-type problems associated with higher-order fractional Laplacians. Our goals are to establish regularity properties of the solution and to describe the structure of the free boundary. To this end, we combine classical techniques from potential theory and the calculus of variations with more modern methods, such as the localization of the operator and monotonicity formulas.