18 citations · 58 across the 17 of their papers we have counts for
23 papers
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 to a PDE of -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…
Fractional -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 -Laplace non-homogeneous equation , with , , for d…
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…
Green function in metric measure spaces
Mario Bonk, Luca Capogna, Xiaodan Zhou
We study existence and uniqueness of Green functions for the Cheeger -Laplacian in metric measure spaces that are Ahlfors -regular and support a -Poincaré inequality with…
Neumann problems for -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 -Laplacians with on any compa…
A Neural Network Ensemble Approach to System Identification
Elisa Negrini, Giovanna Citti, Luca Capogna
We present a new algorithm for learning unknown governing equations from trajectory data, using and ensemble of neural networks. Given samples of solutions to an unknown dyn…