70 citations · 211 across the 16 of their papers we have counts for
17 papers
Klein-Gordon-Born-Infeld equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione +1
In this paper we study a class of Klein-Gordon-Born-Infeld systems in which the classical Laplacian appearing in the matter equation is replaced by a mixed local-nonlocal operator,…
Nontrivial solutions for a class of semilinear elliptic equations with a nonlinear Goldstein-Wentzell boundary condition
Enzo Vitillaro
The paper deals with the existence and multiplicity of nontrivial solutions for the doubly elliptic problem $$\begin{cases} -Δu=f(u) \qquad &\text{in ,}\\ \phantom{-}u=0 &\text{…
Acoustic waves interacting with non--locally reacting surfaces in a Lagrangian framework
Enzo Vitillaro
The paper deals with a family of evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended re…
On the eigenvalue problem for a bulk/surface elliptic system
Enzo Vitillaro
The paper addresses the doubly elliptic eigenvalue problem $$\begin{cases} -Δu=λu \qquad &\text{in ,}\\ u=0 &\text{on ,}\\ -Δ_Γu +\partial_νu =λu\qquad &\text{on ,} \e…
Nontrivial solutions for the Laplace equation with a nonlinear Goldstein-Wentzell boundary condition
Enzo Vitillaro
The paper deals with the existence and multiplicity of nontrivial solutions for the doubly elliptic problem $$\begin{cases} Δu=0 \qquad &\text{in ,}\\ u=0 &\text{on ,}\\ -Δ…
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione +1
In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schröding…
Three evolution problems modelling the interaction between acoustic waves and non-locally reacting surfaces
Enzo Vitillaro
The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The…
Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione +1
Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allo…
The Damped Wave Equation with Acoustic Boundary Conditions and Non-locally Reacting Surfaces
Alessio Barbieri, Enzo Vitillaro
The aim of the paper is to study the problem $$μv_{tt}- \text{div}_Γ(σ\nabla_Γv)+δv_t+κv+ρu_t =0\qquad \text{on $\math…
Blow--up for the wave equation with hyperbolic dynamical boundary conditions, interior and boundary nonlinear damping and sources
Enzo Vitillaro
The aim of this paper is to give global nonexistence and blow--up results for the problem $$ \begin{cases} u_{tt}-Δu+P(x,u_t)=f(x,u) \qquad &\text{in ,}\\ u=0 &\…
The wave equation with acoustic boundary conditions on non-locally reacting surfaces
Delio Mugnolo, Enzo Vitillaro
The aim of the paper is to study the problem in , on , $v_t =\partial_…
Approximation by regular functions in Sobolev spaces arising from doubly elliptic problems
Patrizia Pucci, Enzo Vitillaro
The paper deals with a nontrivial density result for functions, with , in the space $$W^{k,\ell,p}(Ω;Γ)= \left\{u\in W^{k,p}(Ω): u_…
On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources
Enzo Vitillaro
The aim of the paper is to study the problem $$ \begin{cases} u_{tt}-Δu+P(x,u_t)=f(x,u) \qquad &\text{in ,} u=0 &\text{on ,} u_{tt}+\partia…
On the the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and source
Enzo Vitillaro
The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for i…
Blow-up for the wave equation with nonlinear source and boundary damping terms
Alessio Fiscella, Enzo Vitillaro
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data…
Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions
Alessio Fiscella, Enzo Vitillaro
The paper deals with local well-posedness, global existence and blow-up results for reaction--diffusion equations coupled with nonlinear dynamical boundary conditions.
Heat equation with dynamical boundary conditions of reactive-diffusive type
Juan Luis Vázquez, Enzo Vitillaro
This paper deals with the heat equation posed in a bounded regular domain coupled with a dynamical boundary condition of reactive-diffusive type, involving the Laplace-Beltrami ope…