The fractional Lipschitz caloric capacity of Cantor sets

TL;DR

This paper characterizes the fractional Lipschitz caloric capacity of certain Cantor sets in Euclidean space, extending known results from analytic and Riesz capacities despite the heat kernel's asymmetry.

Contribution

It provides a new characterization of s-parabolic Lipschitz caloric capacity for corner-like s-parabolic Cantor sets, bridging gaps with classical capacities.

Findings

Established analogous results to analytic and Riesz capacities

Characterized capacity for corner-like s-parabolic Cantor sets

Extended capacity theory to non-symmetric heat kernels

Abstract

We characterize the s-parabolic Lipschitz caloric capacity of corner-like $s$-parabolic Cantor sets in $\mathbb{R}^{n+1}$ for $1/2<s\leq 1$. Despite the spatial gradient of the s-heat kernel lacking temporal anti-symmetry, we obtain analogous results to those known for analytic and Riesz capacities.