Estimates on Green functions of second order differential operators with singular coefficients

Details Estimates on Green functions of second order differential operators with singular coefficients Estimates on Green functions of second order differential operators with singular coefficients

2005-04-08

arxiv.org/abs/math-ph/0504029v1

Journal of Mathematical Physics, 46(2005)042301

Physics

Mathematical Physics

16 pages

Scientific paper

10.1063/1.1855934

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

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