Green's functions for elliptic and parabolic systems with Robin-type boundary conditions

Abstract

The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's function for parabolic systems with time-dependent coefficients satisfying a possibly nonlocal Robin-type boundary condition assuming that weak solutions of the system are locally Hölder continuous in the interior of the domain, and as a corollary we construct Green's function for elliptic system with a Robin-type condition. Also, we obtain Gaussian bound for Robin Green's function under an additional assumption that weak solutions of Robin problem are locally bounded up to the boundary. We provide some examples satisfying such a local boundedness property, and thus have Gaussian bounds for their Green's functions.

arXiv comment41 pages, accepted in Journal of Functional Analysis

References in corpus (5)

• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• On the Green's matrices of strongly parabolic systems of second order
• Green's function for second order parabolic systems with Neumann boundary condition
• Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients
• Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains

Cited by in corpus (4)

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