On Poisson-Dirichlet problems with polynomial data
Gzyl, Henryk
Publicacions Matemàtiques, Tome 46 (2002), p. 465-471 / Harvested from Biblioteca Digital de Matemáticas
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In this note we provide a probabilistic proof that Poisson and/or Dirichlet problems in an ellipsoid in Rd, that have polynomial data, also have polynomial solutions. Our proofs use basic stochastic calculus. The existing proofs are based on famous lemma by E. Fisher which we do not use, and present a simple martingale proof of it as well.

Publié le : 2002-01-01
DMLE-ID : 3979 
@article{urn:eudml:doc:41460,
     title = {On Poisson-Dirichlet problems with polynomial data},
     journal = {Publicacions Matem\`atiques},
     volume = {46},
     year = {2002},
     pages = {465-471},
     mrnumber = {MR1934365},
     zbl = {1012.60060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41460}
}

Gzyl, Henryk. On Poisson-Dirichlet problems with polynomial data. Publicacions Matemàtiques, Tome 46 (2002) pp. 465-471. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41460/