Estimates on Green functions of second order differential operators with singular coefficients
Abstract
We investigate the Green functions G(x,x) of some second order differential operators on Rd+1 with singular coefficients depending only on one coordinate x0. We express the Green functions by means of the Brownian motion. Applying probabilistic methods we prove that when x=(0, x) and x=(0, x) (here x0=0) lie on the singular hyperplanes then G(0, x;0, x) is more regular than the Green function of operators with regular coefficients.
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