Domenico Vuono

activity

20222026

collaborators

15 papers

math.AP2026

Rigidity results via a Poincaré type formula for stable solutions of quasilinear anisotropic elliptic equations

Berardino Sciunzi, Domenico Vuono

In this paper we prove some one-dimensional symmetry results for stable solutions to quasilinear anisotropic elliptic equations in $R^{2}$ and $R^{3}$ . In this regard,…

math.AP2026

On the second-order regularity of widely degenerate elliptic systems

Felice Iandoli, Berardino Sciunzi, Domenico Vuono

We prove local second-order regularity near the critical set for widely degenerate elliptic systems, and show that this degenerate region has zero Lebesgue measure provided the sou…

math.AP2026

Classification of singular solutions to the subcritical Lane-Emden equation in $R^{N} ∖ {0}$

Francesco Esposito, Luigi Muglia, Berardino Sciunzi +1

We provide a classification result of positive solutions with a non-removable singularity at the origin to the subcritical Lane-Emden equation $- Δ_{p} u = u^{q}$ in $\mathbb{R}^N \setm…

math.AP2026

Local bounds for nonlinear higher-order vector fields for the p-Laplace equation

Felice Iandoli, Giuseppe Spadaro, Domenico Vuono

We study higher regularity for weak solutions of the $p$ -Laplace equation $- Δ_{p} u = f$ in a domain $Ω \subset R^{n}$ for $p$ sufficiently close to 2. For $m \geq 3$ , assuming…

math.AP2025

Monotonicity and Liouville-type theorems for semilinear elliptic problems in the half space

Berardino Sciunzi, Domenico Vuono

We consider classical solutions to $- Δ u = f (u)$ in half-spaces, under homogeneous Dirichlet boundary conditions. We prove that any positive solution is strictly monotone increasing…

math.AP2025

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Giuseppe Spadaro, Domenico Vuono

We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrabi…

math.AP2025

Global second order optimal regularity for the vectorial $p$ -Laplacian

Berardino Sciunzi, Giuseppe Spadaro, Domenico Vuono

We obtain optimal regularity results for solutions to vectorial $p$ -Laplace equations $$ -{\boldsymbol Δ}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsy…

math.AP2025

Local behaviour of the second order derivatives of solutions to $p$ -Laplace equations

Felice Iandoli, Domenico Vuono

We consider the equation $- Δ_{p} u = f (x)$ in $Ω,$ where $Δ_{p}$ is the $p$ -Laplace operator. We provide $L^{\infty}$ -type estimates for the second derivatives of solutions when $…

math.AP2025

Harnack inequalities for quasilinear anisotropic elliptic equations with a first order term

Domenico Vuono

We consider weak solutions of the equation $- Δ_{p}^{H} u + a (x, u) H^{q} (\nabla u) = f (x, u) in Ω,$ where $H$ is in some cases called Finsler norm, $Ω$ is a domain of $\mathbb R…

math.AP2024

Second order regularity for solutions to anisotropic degenerate elliptic equations

Daniel Baratta, Luigi Muglia, Domenico Vuono

We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity resu…

math.AP2024

Third order estimates and the regularity of the stress field for solutions to $p$ -Laplace equations

Daniel Baratta, Berardino Sciunzi, Domenico Vuono

We consider solutions to $- Δ_{p} u = f (x) in Ω,$ when $p$ approaches the semilinear limiting case $p = 2$ and we get third order estimates. As a consequence we d…

math.AP2023

Regularity and symmetry results for the vectorial p-Laplacian

Luigi Montoro, Luigi Muglia, Berardino Sciunzi +1

We obtain some regularity results for solutions to vectorial $p$ -Laplace equations $$ -{\boldsymbol Δ}_p{\boldsymbol u}=-\operatorname{\bf div}(|D{\boldsymbol u}|^{p-2}D{\boldsymbo…

math.AP2023

Asymptotic behaviour of solutions to the anisotropic doubly critical equation

Francesco Esposito, Luigi Montoro, Berardino Sciunzi +1

The aim of this paper is to deal with the anisotropic doubly critical equation $- Δ_{p}^{H} u - \frac{γ}{[ H ^{\circ} ( x ) ] ^{p}} u^{p - 1} = u^{p^{*} - 1} in R^{N},$ where $H$ is in som…

math.AP2023

Liouville-type results for some quasilinear anisotropic elliptic equations

Alberto Farina, Berardino Sciunzi, Domenico Vuono

We prove some Liouville-type theorems for stable solutions (and solutions stable outside a compact set) of quasilinear anisotropic elliptic equations. Our results cover the particu…

math.AP2022

Anisotropic Kelvin-type transform for a class of anisotropic elliptic operators

Francesco Esposito, Giuseppe Riey, Berardino Sciunzi +1

In this paper we introduce and study a new Kelvin-type transform in the anisotropic setting. In particular, we deal with semilinear and quasilinear anisotropic elliptic problems in…

Rigidity results via a Poincaré type formula for stable solutions of quasilinear anisotropic elliptic equations

On the second-order regularity of widely degenerate elliptic systems

Classification of singular solutions to the subcritical Lane-Emden equation in RN∖{0}

Local bounds for nonlinear higher-order vector fields for the p-Laplace equation

Monotonicity and Liouville-type theorems for semilinear elliptic problems in the half space

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Global second order optimal regularity for the vectorial p-Laplacian

Local behaviour of the second order derivatives of solutions to p-Laplace equations

Harnack inequalities for quasilinear anisotropic elliptic equations with a first order term

Second order regularity for solutions to anisotropic degenerate elliptic equations

Third order estimates and the regularity of the stress field for solutions to p-Laplace equations

Regularity and symmetry results for the vectorial p-Laplacian

Asymptotic behaviour of solutions to the anisotropic doubly critical equation

Liouville-type results for some quasilinear anisotropic elliptic equations

Anisotropic Kelvin-type transform for a class of anisotropic elliptic operators

Classification of singular solutions to the subcritical Lane-Emden equation in $R^{N} ∖ {0}$

Global second order optimal regularity for the vectorial $p$ -Laplacian

Local behaviour of the second order derivatives of solutions to $p$ -Laplace equations

Third order estimates and the regularity of the stress field for solutions to $p$ -Laplace equations