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

collaborators

Showing 2022Show all

3 papers · 1 filter

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…

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

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