Resumen de Definition of fractional Laplacian for functions with polynomial growth

Serena Dipierro, Ovidiu Savin, Enrico Valdinoci

• We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheless, we can give an ad-hoc definition, which (in addition to the various results that we prove here) can also be useful for applications in various fields, such as blowup and free boundary problems.