Alessandro Goffi

Regularizing estimates for positive solutions of the heat equation under geometric flows

Alessandro Goffi, Francesco Pediconi

We study higher-order global estimates for the heat equation on Riemannian manifolds, both for static metrics and for metrics evolving under the Ricci flow. Under minimal geometric…

On the rate of the vanishing viscosity approximation for Mean Field Games with nonlocal coupling

Gennaro Ciampa, Alessandro Goffi

We study quantitative convergence rates of the vanishing viscosity approximation of first-order time-dependent Mean Field Games with regularizing coupling acting in the Hamilton-Ja…

Quantitative maximal $L^{2}$ -regularity for viscous Hamilton-Jacobi PDEs in 2D and Mean Field Games

Alessandro Goffi

We discuss quantitative Calderón-Zygmund estimates in $W^{2, 2}$ for 2D viscous Hamilton-Jacobi equations with natural growth in the gradient. We apply the result to obtain the exis…

Transport-diffusion equations with irregular data and applications to stability estimates for second-order Hamilton-Jacobi PDEs

Gianmarco Giovannardi, Alessandro Goffi

This paper studies quantitative uniqueness properties in $L^{p}$ spaces for Fokker-Planck and transport-diffusion equations under two new assumptions on their velocity field $b=b(x,t…

On the smoothness of solutions of fully nonlinear second order equations in the plane

Alessandro Goffi

We study interior $C^{2, α}$ regularity estimates for solutions of fully nonlinear uniformly elliptic equations of the general form $F (D^{2} u) = 0$ in two independent variables and with…

math.AP2025

Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations

Alekos Cecchin, Alessandro Goffi

We obtain new quantitative estimates of the vanishing viscosity approximation for time-dependent, degenerate, Hamilton-Jacobi equations that are neither concave nor convex in the g…

math.AP2025

Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions

Alessandro Goffi

We study the quantitative small noise limit in the $L^{\infty}$ norm of certain time-dependent Hamilton-Jacobi equations equipped with Neumann boundary conditions, depending on the r…

math.AP2025

Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case

Marco Cirant, Alessandro Goffi

We study the speed of convergence in $L^{\infty}$ norm of the vanishing viscosity process for Hamilton-Jacobi equations with uniformly or strictly convex Hamiltonian terms with super…

math.AP2024

Remarks on the rate of convergence of the vanishing viscosity process of Hamilton-Jacobi equations

Alessandro Goffi

We establish a linear $L^{p}$ rate of convergence, $1 < p < \infty$ , with respect to the viscosity $ε$ for the vanishing viscosity process of semiconcave solutions of Hamilton-…

math.AP2024

Global geometric estimates for the heat equation via duality methods

Alessandro Goffi, Giulio Tralli

We discuss first-order and second-order regularization effects for solutions to the classical heat equation. In particular we propose a global approach to study smoothing effects o…

math.AP2024

Interpolated time-Hölder regularity of solutions of fully nonlinear parabolic equations

Alessandro Goffi

We show interior Schauder estimates for a special class of fully nonlinear parabolic Isaacs equations by the maximum principle, providing an Evans-Krylov result for the model equat…

Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth

Alessandro Goffi

We establish local Hölder estimates for viscosity solutions of fully nonlinear second order equations with quadratic growth in the gradient and unbounded right-hand side in $L^{q}$ s…

Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method

Fabio Camilli, Alessandro Goffi, Cristian Mendico

We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^{p}$ -rates of convergence for the vanishing vis…

Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions

Alessandro Goffi

In this note, we prove interior a priori first- and second-order estimates for solutions of fully nonlinear degenerate elliptic inequalities structured over the vector fields of Ca…

High-order estimates for fully nonlinear equations under weak concavity assumptions

Alessandro Goffi

This paper studies a priori and regularity estimates of Evans-Krylov type in Hölder spaces for fully nonlinear uniformly elliptic and parabolic equations of second order when the o…

math.AP2022

Gradient estimates for quasilinear elliptic Neumann problems with unbounded first-order terms

Marco Cirant, Alessandro Goffi, Tommaso Leonori

This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$ -Laplacian with first-order terms having polynomial growth with respect to…

math.AP2022

A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method

Alessandro Goffi

We establish a priori Lipschitz estimates for equations with mixed local and nonlocal diffusion, coercive gradient terms and unbounded right-hand side in Lebesgue spaces through an…

math.AP2022

Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms

Alessandro Goffi

This note studies local integral gradient bounds for distributional solutions of a large class of partial differential inequalities with diffusion in divergence form and power-like…

math.AP2021★ 1 cited

On the optimal $L^{q}$ -regularity for viscous Hamilton-Jacobi equations with subquadratic growth in the gradient

Alessandro Goffi

This paper studies a maximal $L^{q}$ -regularity property for nonlinear elliptic equations of second order with a zero-th order term and gradient nonlinearities having superlinear and…

Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds

Alessandro Goffi, Francesco Pediconi

In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented w…

Liouville results for fully nonlinear equations modeled on Hörmander vector fields: II. Carnot groups and Grushin geometries

Martino Bardi, Alessandro Goffi

The paper treats second order fully nonlinear degenerate elliptic equations having a family of subunit vector fields satisfying a full-rank bracket condition. It studies Liouville…

On the Liouville property for fully nonlinear equations with superlinear first-order terms

Marco Cirant, Alessandro Goffi

We consider in this note one-side Liouville properties for viscosity solutions of various fully nonlinear uniformly elliptic inequalities, whose prototype is $F(x,D^2u)\geq H_i(x,u…