Michele Gatti

collaborators

7 papers

math.AP2026

The Liouville equation on Riemannian surfaces: the role of volume growth in classification and rigidity results

Giulio Ciraolo, Alberto Farina, Michele Gatti

We study the Liouville equation $- I^ u = e^{u}$ on a complete, connected, non-compact, boundaryless Riemannian surface $(M, g)$ with non-negative Ricci curvature. Assuming only some a…

math.AP2026

On the anisotropic critical $p$ -Laplace equation: classification, decomposition, and stability results

Carlo Alberto Antonini, Giulio Ciraolo, Michele Gatti

We investigate both qualitative and quantitative issues related to the classification of non-negative energy solutions to the anisotropic critical $p$ -Laplace equation in $\mathbb{…

math.AP2026

Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition

Michele Gatti, Julian Scheuer, Tobias Weth

We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $Î©\subseteq \…

math.AP2026

Classification results for bounded positive solutions to the critical $p$ -Laplace equation

Giulio Ciraolo, Michele Gatti

By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$ -Laplace equation in $…

math.AP2025

On the stability of the critical $p$ -Laplace equation

Giulio Ciraolo, Michele Gatti

For $1 < p < n$ , it is well-known that non-negative, energy weak solutions to $I^_{p} u + u^{p^{*} - 1} = 0$ in $R^{n}$ are completely classified. Moreover, due to a fundamental r…

math.AP2025

Approximate radial symmetry for $p$ -Laplace equations via the moving planes method

Michele Gatti

We investigate quasi-symmetry for small perturbations of the Gidas-Ni-Nirenberg problem involving the $p$ -Laplacian and for small perturbations the critical $p$ -Laplace equation fo…

The Liouville equation on Riemannian surfaces: the role of volume growth in classification and rigidity results

On the anisotropic critical p-Laplace equation: classification, decomposition, and stability results

Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition

Classification results for bounded positive solutions to the critical p-Laplace equation

On the stability of the critical p-Laplace equation

Approximate radial symmetry for p-Laplace equations via the moving planes method

On the anisotropic critical $p$ -Laplace equation: classification, decomposition, and stability results

Classification results for bounded positive solutions to the critical $p$ -Laplace equation

On the stability of the critical $p$ -Laplace equation

Approximate radial symmetry for $p$ -Laplace equations via the moving planes method