9 papers
Blow-up of solutions to semilinear parabolic equations driven by mixed local-nonlocal operators with large initial data
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We investigate finite-time blow-up for nonnegative solutions to the Cauchy problem associated with semilinear parabolic equations driven by a mixed local--nonlocal operator. The re…
Existence and uniqueness of weak solutions to singular anisotropic elliptic problems
Francesco Esposito, Francescantonio Oliva, Eugenio Vecchi
In this paper we consider a quasilinear singular anisotropic elliptic problem with a p-sublinear perturbation. We prove uniqueness of weak solutions and we provide necessary and su…
On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed op…
Critical concave-convex problems in Carnot groups
Mattia Galeotti, Eugenio Vecchi
We consider a model Dirichlet problem with concave-convex and critical nonlinearity settled in Carnot groups. Our aim is to prove the existence of two positve solutions in the spir…
Regularizing effects of absorption terms in local-nonlocal mild singular problems
Stefano Biagi, Enzo Maria Merlino, Eugenio Vecchi
In this paper we prove existence and uniqueness of energy solutionns for singular problems with absorption driven by local-nonlocal operators. Moreover, we establish a comparison p…
Critical singular problems in Carnot groups
Stefano Biagi, Mattia Galeotti, Eugenio Vecchi
We consider a power-type mild singular perturbation of a Dirichlet semilinear critical problem settled in an open and bounded set in a Carnot group. Here, the term critical has to…
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 weak solutions for the inverse mean curvature flow in the Heisenberg group
Adriano Pisante, Eugenio Vecchi
We consider the inverse mean curvature flow (IMCF) in the Heisenberg group $(\He^n, d_\varepsilon)$, where is distance associated to either ,…