Green's functions for parabolic systems of second order in time-varying domains

Abstract

We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and 1/2-Hölder continuous in the time variable, under the assumption that weak solutions of the system satisfy an interior Hölder continuity estimate. We also derive global pointwise estimates for Green's function in such time-varying domains under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Hölder continuity estimate. In particular, our results apply to complex perturbations of a single real equation.

25 pages, 0 figure

References in corpus (5)

• The Green function estimates for strongly elliptic systems of second order
• 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
• 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