Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces

TY - UNPB

T1 - Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces

AU - Ruiz, Patricia Alonso

AU - Baudoin, Fabrice

N1 - 26 pages

PY - 2024/1/28

Y1 - 2024/1/28

N2 - This paper studies properties of $\Gamma$-limits of Korevaar-Schoen $p$-energies on a Cheeger space. When $p>1$, this kind of limit provides a natural $p$-energy form that can be used to define a $p$-Laplacian, and whose domain is the Newtonian Sobolev space $N^{1,p}$. When $p=1$, the limit can be interpreted as a total variation functional whose domain is the space of BV functions. When the underlying space is compact, the $\Gamma$-convergence of the $p$-energies is improved to Mosco convergence for every $p \ge 1$.

AB - This paper studies properties of $\Gamma$-limits of Korevaar-Schoen $p$-energies on a Cheeger space. When $p>1$, this kind of limit provides a natural $p$-energy form that can be used to define a $p$-Laplacian, and whose domain is the Newtonian Sobolev space $N^{1,p}$. When $p=1$, the limit can be interpreted as a total variation functional whose domain is the space of BV functions. When the underlying space is compact, the $\Gamma$-convergence of the $p$-energies is improved to Mosco convergence for every $p \ge 1$.

KW - math.FA

KW - math.AP

KW - math.MG

KW - 30L99, 31C45, 46E36, 47H99

M3 - Preprint

BT - Korevaar-Schoen $p$-energies and their $Γ$-limits on Cheeger spaces

ER -