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math.PR2023
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
Naotaka Kajino, Mathav Murugan
We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion o…
math.MG2023
First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet
Mathav Murugan, Ryosuke Shimizu
We construct and investigate -Sobolev space, -energy, and the corresponding -energy measures on the planar Sierpiński carpet for all . Our method i…
math.PR2023
Heat kernel for reflected diffusion and extension property on uniform domains
Mathav Murugan
We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of J…