6 papers
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…
Local boundedness for solutions of a class of non-uniformly elliptic anisotropic problems
Stefano Biagi, Giovanni Cupini, Elvira Mascolo
We consider a class of {energy integrals}, associated to nonlinear and non-uniformly elliptic equations, with integrands satisfying anisotropic -growth condition…
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…
A Brezis-Nirenberg type result for mixed local and nonlocal operators
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. In particular, we investigate the corresponding…
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…