7 papers · 1 filter
Brezis-Nirenberg-type results for the anisotropic -Laplacian
Stefano Biagi, Francesco Esposito, Alberto Roncoroni +1
In this paper we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic -Laplacian. The critical exponent is the…
On mixed local-nonlocal problems with Hardy potential
Stefano Biagi, Francesco Esposito, Luigi Montoro +1
In this paper we study the effect of the Hardy potential on existence, uniqueness and optimal summability of solutions of the mixed local-nonlocal elliptic problem $$-Δu + (-Δ)^s u…
Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator , with a power-like source term.…
Phragmèn-Lindelöf type theorems for elliptic equations on infinite graphs
Stefano Biagi, Fabio Punzo
We investigate the validity of the Phragmèn-Lindelöf principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the…
On the existence of a second positive solution to mixed local-nonlocal concave-convex critical problems
Stefano Biagi, Eugenio Vecchi
We prove the existence of a second positive weak solution for mixed local-nonlocal critical semilinear elliptic problems with a sublinear perturbation in the spirit of [Ambrosetti,…
A Liouville theorem for elliptic equations with a potential on infinite graphs
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on t…