Heat kernel estimates for regional fractional Laplacians with multi-singular critical potentials in C1,β open sets

Renming Song, Peixue Wu and Shukun Wu

Stochastic Processes and their Applications, 2025, vol. 189, issue C

Abstract: Let D be an open set of Rd, α∈(0,2) and let LαD be the generator of the censored α-stable process in D. In this paper, we establish sharp two-sided heat kernel estimates for LαD−κ, with κ being a non-negative critical potential and D being a C1,β open set, β∈((α−1)+,1]. The potential κ can exhibit multi-singularities and our regularity assumption on D is weaker than the regularity assumed in earlier literature on heat kernel estimates of fractional Laplacians.

Keywords: Heat kernel; Regional fractional Laplacian; Critical potentials (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104727

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