Eigenvalues for a combination between local and nonlocal $p-$Laplacians

Leandro M. Del Pezzo, Raul Ferreira, Julio Rossi

In this paper we study the Dirichlet eigenvalue problem $$-{\Delta }_{p}u-{\Delta }_{J,p}u=\lambda |u{|}^{p-2}u\text{ in }\Omega ,u=0\text{ in }{\Omega }^c={\mathbb{R}}^N\setminus \Omega .$$ Here ${\Delta }_{p}u$ i…