Domenico Vuono

collaborators

6 papers

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…

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

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

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