A Brezis-Nirenberg type result for mixed local and nonlocal operators

Stefano Biagi, Serena Dipierro, Enrico Valdinoci, Eugenio Vecchi

Published 2022-09-15Version 1

We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.