8 papers · 1 filter
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…
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…
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…
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 ,…
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…