L. Capogna

activity

20082025

most citedRegularity of non-characteristic minimal graphs in the Heisenberg group

H^{1}

18 citations · 58 across the 17 of their papers we have counts for

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19 papers · 1 filter

math.AP2025

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

Luca Capogna, Ryan Gibara, Riikka Korte +1

We prove global Hölder regularity result for weak solutions $u \in N^{1, p} (Ω, μ)$ to a PDE of $p$ -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…

math.AP2024

Fractional $p$ -Laplacians via Neumann problems in unbounded metric measure spaces

Luca Capogna, Ryan Gibara, Riikka Korte +1

We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional $p$ -Laplace non-homogeneous equation $(- Δ_{p})^{s} u = f$ , with $0 < s < 1$ , $1 < p < \infty$ , for d…

math.AP2022

Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group

Luca Capogna, Giovanna Citti, Xiao Zhong

This note provides a succinct survey of the existing literature concerning the Hölder regularity for the gradient of weak solutions of PDEs of the form $$\sum_{i=1}^{2n} X_i A_i(\n…

math.AP2022

Green function in metric measure spaces

Mario Bonk, Luca Capogna, Xiaodan Zhou

We study existence and uniqueness of Green functions for the Cheeger $Q$ -Laplacian in metric measure spaces that are Ahlfors $Q$ -regular and support a $Q$ -Poincaré inequality with…

math.AP2022★ 7 cited

Neumann problems for $p$ -harmonic functions, and induced nonlocal operators in metric measure spaces

Luca Capogna, Josh Kline, Riikka Korte +2

Following ideas of Caffarelli and Silvestre in~\cite{CS}, and using recent progress in hyperbolic fillings, we define fractional $p$ -Laplacians $(- Δ_{p})^{θ}$ with $0 < θ < 1$ on any compa…

math.AP2021

Lipschitz regularity for solutions of the parabolic $p$ -Laplacian in the Heisenberg group

Luca Capogna, Giovanna Citti, Xiao Zhong

We prove local Lipschitz regularity for weak solutions to a class of degenerate parabolic PDEs modeled on the parabolic $p$ -Laplacian $$\p_t u= \sum_{i=1}^{2n} X_i (|\nabla_0 u|^{p…

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

Fractional p-Laplacians via Neumann problems in unbounded metric measure spaces

Regularity theory of quasilinear elliptic and parabolic equations in the Heisenberg group

Green function in metric measure spaces

Neumann problems for p-harmonic functions, and induced nonlocal operators in metric measure spaces

Lipschitz regularity for solutions of the parabolic p-Laplacian in the Heisenberg group

Fractional $p$ -Laplacians via Neumann problems in unbounded metric measure spaces

Neumann problems for $p$ -harmonic functions, and induced nonlocal operators in metric measure spaces

Lipschitz regularity for solutions of the parabolic $p$ -Laplacian in the Heisenberg group