On the Green's matrices of strongly parabolic systems of second order

Abstract

We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems satisfy an interior Hölder continuity estimate. We present a unified approach valid for both the scalar and the vectorial cases.

33 pages

References in corpus (1)

• Gaussian estimates for fundamental solutions of second order parabolic systems with time-independent coefficients

Cited by in corpus (4)

• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains
• A Mathematical Guide to Operator Learning
• Green's functions for elliptic and parabolic systems with Robin-type boundary conditions
• Estimates for fundamental solutions of parabolic equations in non-divergence form