Small-time heat decay for stable processes on fractal drums
Abstract
In this paper, we study the spectral heat content for isotropic stable processes on fractal drums (namely, open sets with fractal boundaries). The spectral heat content for subordinate killed Brownian motions by stable subordinators was investigated in PX23, and the present work serves as a natural extension of PX23 for the spectral heat content for stable processes. Under suitable geometric conditions on the underlying domains, we show that the decay rate of the spectral heat content for stable processes differs substantially from that for subordinate killed Brownian motions when α=d-, where is the interior Minkowski dimension of the boundary of the underlying open set.
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