Eugenio Vecchi
YOU?
Author Swipe
View article: Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian
Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian Open
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 usual such that the embedding is not compact. We prove the ex…
View article: Regularizing effects of absorption terms in local-nonlocal mild singular problems
Regularizing effects of absorption terms in local-nonlocal mild singular problems Open
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 principle à la Talenti, leading to a gain of summability res…
View article: Critical singular problems in Carnot groups
Critical singular problems in Carnot groups Open
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 be understood in the sense of the Sobolev embedding. We aim…
View article: A Brezis-Nirenberg type result for mixed local and nonlocal operators
A Brezis-Nirenberg type result for mixed local and nonlocal operators Open
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 Sobolev inequality, detecting the optimal constant, which …
View article: Global solutions to semilinear parabolic equations driven by mixed local–nonlocal operators
Global solutions to semilinear parabolic equations driven by mixed local–nonlocal operators Open
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. We show that the so‐called Fujita phenomenon holds, and the critical value is exact…
View article: Brezis-Nirenberg-type results for the anisotropic $p$-Laplacian
Brezis-Nirenberg-type results for the anisotropic $p$-Laplacian Open
In this paper we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic $p$-Laplacian. The critical exponent is the usual $p^{\star}$ such that the embedding $W^{1,p}_{0}(Ω) \…
View article: On mixed local-nonlocal problems with Hardy potential
On mixed local-nonlocal problems with Hardy potential Open
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 - γ\frac{u}{|x|^2}=f \text{ in } Ω, \ u=0 \text{ in } \mat…
View article: Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators Open
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator $\mathcal{L} = -Δ+(-Δ)^s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and th…
View article: Global weak solutions for the inverse mean curvature flow in the Heisenberg group
Global weak solutions for the inverse mean curvature flow in the Heisenberg group Open
We consider the inverse mean curvature flow (IMCF) in the Heisenberg group $(\He^n, d_\varepsilon)$, where $d_\varepsilon$ is distance associated to either $| \cdot |_\varepsilon$, $\varepsilon>0$, the natural family of left-invariant Riem…
View article: On the existence of a second positive solution to mixed local-nonlocal concave-convex critical problems
On the existence of a second positive solution to mixed local-nonlocal concave-convex critical problems Open
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, Brezis, Cerami, 1994].
View article: Symmetry and monotonicity of singular solutions to <i>p</i>-Laplacian systems involving a first order term
Symmetry and monotonicity of singular solutions to <i>p</i>-Laplacian systems involving a first order term Open
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by p -Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version…
View article: On a Brezis-Oswald-type result for degenerate Kirchhoff problems
On a Brezis-Oswald-type result for degenerate Kirchhoff problems Open
In the present note we establish an almost-optimal solvability result for Kirchhoff-type problems of the following form{--M (||Delta u||L2(Omega)) = u= fz(x,u) in f(x, u) in Omega,u >=, L2(omega) u > 0, in Omega u = 0 on partial deri…
View article: Multiplicity of positive solutions for mixed local-nonlocal singular critical problems
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems Open
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], extending the recent results in [Garain, 2023] concerning singular …
View article: An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems
An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems Open
We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A caref…
View article: An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems
An Ahmad-Lazer-Paul-type result for indefinite mixed local-nonlocal problems Open
We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A caref…
View article: Variational methods for nonpositive mixed local–nonlocal operators
Variational methods for nonpositive mixed local–nonlocal operators Open
We prove the existence of a weak solution for boundary value problems driven by a mixed local–nonlocal operator. The main novelty is that such an operator is allowed to be nonpositive definite.
View article: Symmetry of intrinsically singular solutions of double phase problems
Symmetry of intrinsically singular solutions of double phase problems Open
We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case p < q < 2, and we relax the assumption on the capacity of the singular set using a…
View article: G-convergence of elliptic and parabolic operators depending on vector fields
G-convergence of elliptic and parabolic operators depending on vector fields Open
We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G -convergence, or H -convergence, by means of the compensated compactness…
View article: A Brezis-Nirenberg type result for mixed local and nonlocal operators
A Brezis-Nirenberg type result for mixed local and nonlocal operators Open
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 Sobolev inequality, detecting the optimal constant, which …
View article: A Brezis–Oswald approach for mixed local and nonlocal operators
A Brezis–Oswald approach for mixed local and nonlocal operators Open
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 quasilinear local and a nonlocal operator, i.e. [Formula: see t…
View article: Variational methods for nonpositive mixed local-nonlocal operators
Variational methods for nonpositive mixed local-nonlocal operators Open
We prove the existence of a weak solution for boundary value problems driven by a mixed local--nonlocal operator. The main novelty is that such an operator is allowed to be nonpositive definite.
View article: Symmetry of intrinsically singular solutions of double phase problems
Symmetry of intrinsically singular solutions of double phase problems Open
We continue the study of positive singular solutions of PDEs arising from double phase functionals started in [6]. In particular, we consider the case $p
View article: Symmetry and monotonicity of singular solutions to $p$-Laplacian systems involving a first order term
Symmetry and monotonicity of singular solutions to $p$-Laplacian systems involving a first order term Open
We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by $p$-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new versio…
View article: A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators
A Hong-Krahn-Szegö inequality for mixed local and nonlocal operators Open
Given a bounded open set $ \Omega\subseteq{\mathbb{R}}^n $, we consider the eigenvalue problem for a nonlinear mixed local/nonlocal operator with vanishing conditions in the complement of $ \Omega $. We prove that the second eigenvalue $ \…
View article: Mixed local and nonlocal elliptic operators: regularity and maximum principles
Mixed local and nonlocal elliptic operators: regularity and maximum principles Open
We start in this paper a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the Laplacian and the fractional Laplacian, an…
View article: On the asymptotic behavior of $p$-fractional eigenvalues
On the asymptotic behavior of $p$-fractional eigenvalues Open
In this note we obtain an asymptotic estimate for growth behavior of variational eigenvalues of the $p-$fractional eigenvalue problem on a smooth bounded domain with Dirichlet boundary condition.