Dirichlet-to-Neumann and elliptic operators on C1+-domains: Poisson and Gaussian bounds

Volume: 267, Issue: 7, Pages: 4224 - 4273
Published: Sep 1, 2019
Abstract
We prove Poisson upper bounds for the heat kernel of the Dirichlet-to-Neumann operator with variable Hölder coefficients when the underlying domain is bounded and has a C 1 + κ -boundary for some κ > 0 . We also prove a number of other results such as gradient estimates for heat kernels and Green functions G of elliptic operators with possibly complex-valued coefficients. We establish Hölder continuity of ∇ x ∇ y G up to the boundary. These...
Paper Details
Title
Dirichlet-to-Neumann and elliptic operators on C1+-domains: Poisson and Gaussian bounds
Published Date
Sep 1, 2019
Volume
267
Issue
7
Pages
4224 - 4273
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