Estimates of Dirichlet heat kernels

Feng-Yu Wang

Stochastic Processes and their Applications, 1998, vol. 74, issue 2, 217-234

Abstract: By using logarithmic transformations and stochastic analysis, an explicit lower bound of Dirichlet heat kernels is obtained, which can be sharp for both short time and long time. Next, a two-side comparison theorem is presented for Dirichlet heat kernels and some closed ones, from which we derive the Bismut's type derivative formula for Dirichlet heat kernels. Moreover, the Li-Yau's type Harnack inequality is established for Dirichlet heat semigroups. Finally, the integration estimate of Dirichlet heat kernels is also studied.

Keywords: Dirichlet; heat; kernel; Diffusion; process; Gradient; estimate; Harnack; inequality (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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