Dirichlet-to-Neumann and elliptic operators on C 1+κ -domains: Poisson and Gaussian bounds
Language
en
Article de revue
This item was published in
Journal of Differential Equations. 2019
Elsevier
English 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 ...Read more >
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 results are used to prove L p-estimates for commutators of Dirichlet-to-Neumann operators on the boundary of C 1+κ-domains. Such estimates are the keystone in our approach for the Poisson bounds.Read less <
English Keywords
58G11
AMS Subject Classification: 35K08
47B47
Keywords: Dirichlet-to-Neumann operator
Poisson bounds
elliptic operators with com-
plex coefficients
heat kernel bounds
gradient estimates for Green functions
commutator
estimates
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