Estimates on Green functions of second order differential operators with singular coefficients
Haba, Z.
arXiv, 0504029 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-04-08
Classification:  Mathematical Physics,  High Energy Physics - Theory 
@article{0504029,
     author = {Haba, Z.},
     title = {Estimates on Green functions of second order differential operators with
  singular coefficients},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504029}
}

Haba, Z. Estimates on Green functions of second order differential operators with
  singular coefficients. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504029/