Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs
On a Sobolev critical problemfor the superposition of a local and nonlocal operator with the wrong sign
Eugenio Vecchi
ALMA MATER STUDIORUM - Universita' di Bologna Italy
Co-Author(s):
Abstract:
In this talk I will focus on a Sobolev critical problems in a bounded domain where the operator is given by th $-\Delta - (-\Delta)^s$ with $s\in (0,1)$, possibly losing the maximum principles. I will discuss the existence of at least one non trivial solution.
The talk is based on a joint work with S. Biagi, S. Dipierro and E. Valdinoci.