25 citations · 69 across the 37 of their papers we have counts for
42 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 conditions…
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 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,…
Global Sobolev regularity for nonvariational operators built with homogeneous Hörmander vector fields
Stefano Biagi, Marco Bramanti
We consider a class of nonvariational degenerate elliptic operators of the kind \[ Lu=\sum_{i,j=1}^{m}a_{ij}\left( x\right) X_{i}X_{j}u \] where $\left\{ a_{ij}\left( x\right) \rig…
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems
Stefano Biagi, Eugenio Vecchi
We prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of [Haitao, 2003], extendin…
Uniqueness for local-nonlocal elliptic equations
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We study mixed local and nonlocal elliptic equation with a variable coefficient . Under suitable assumptions on the behaviour at infinity of , we obtain uniqueness of solutio…
KFP operators with coefficients measurable in time and Dini continuous in space
Stefano Biagi, Marco Bramanti, Bianca Stroffolini
We consider degenerate KFP operators \[ Lu=\sum_{i,j=1}^{m_{0}}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partial_{t}u\equiv\sum_{i,j=1}^{m…
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…
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…
Schauder estimates for Kolmogorov-Fokker-Planck operators with coefficients measurable in time and Hölder continuous in space
Stefano Biagi, Marco Bramanti
We consider degenerate Kolmogorov-Fokker-Planck operators $$ \mathcal{L}u=\sum_{i,j=1}^{q}a_{ij}(x,t)\partial_{x_{i}x_{j}}^{2}u+\sum_{k,j=1}^{N}b_{jk}x_{k}\partial_{x_{j}}u-\partia…
Symmetry of intrinsically singular solutions of double phase problems
Stefano Biagi, Francesco Esposito, Eugenio Vecchi
We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case , and we relax the a…
Symmetry and monotonicity of singular solutions to -Laplacian systems involving a first order term
Stefano Biagi, Francesco Esposito, Luigi Montoro +1
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by -Laplacian operators and with the additional presence of a nonlinea…
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
Given a bounded open set , we consider the eigenvalue problem of a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of…
A Faber-Krahn inequality for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that…
A Brezis-Oswald approach for mixed local and nonlocal operators
Stefano Biagi, Dimitri Mugnai, Eugenio Vecchi
In this paper we provide necessary and sufficient conditions for the existence of a unique positive weak solution for some sublinear Dirichlet problems driven by the sum of a quasi…
Non-divergence operators structured on homogeneous Hörmander vector fields: heat kernels and global Gaussian bounds
Stefano Biagi, Marco Bramanti
Let be a family of real smooth vector fields defined in , -homogeneous with respect to a nonisotropic family of dilations and satisfying Hörman…
Symmetry and monotonicity of singular solutions of double phase problems
Stefano Biagi, Francesco Esposito, Eugenio Vecchi
We consider positive singular solutions of PDEs arising from double phase functionals. Exploiting a rather new version of the moving plane method originally developed by Sciunzi, w…
Nonzero positive solutions of fractional Laplacian systems with functional terms
Stefano Biagi, Alessandro Calamai, Gennaro Infante
We study the existence of non-zero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian. Our approach is based on the not…