Spectral heat content for α-stable processes in C1,1 open sets

2020/07/06 by Park, Hyunchul, Song, Renming
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.02815

Abstract

In this paper we study the asymptotic behavior, as t\downarrow 0, of the spectral heat content Q^(α)_D(t) for isotropic α-stable processes, α∈ [1,2), in bounded C^1,1 open sets D⊂ \R^d, d≥ 2. Together with the results from \citeVal2017 for d=1 and \citeGPS19 for α∈ (0,1), the main theorem of this paper establishes the asymptotic behavior of the spectral heat content up to the second term for all α∈ (0,2) and d≥1, and resolves the conjecture raised in \citeVal2017.

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