TER ELST, A.F.M.; OUHABAZ, El Maati

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TER ELST, A.F.M.
University of Auckland [Auckland]

OUHABAZ, El Maati
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Differential Equations. 2019

Elsevier

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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.< Leer menos

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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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Dirichlet-to-Neumann and elliptic operators on C 1+κ -domains: Poisson and Gaussian bounds

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