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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.
@article{Gzyl2002, abstract = {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.}, author = {Gzyl, Henryk}, journal = {Publicacions Matemàtiques}, keywords = {Ecuaciones diferenciales estocásticas; Integración estocástica; Problemas de valor de frontera; Problema de Dirichlet; Ecuación de Poisson; Funciones polinómicas; Poisson-Dirichlet problems; stochastic calculus}, language = {eng}, number = {2}, pages = {465-471}, title = {On Poisson-Dirichlet problems with polynomial data}, url = {http://eudml.org/doc/41460}, volume = {46}, year = {2002}, }
TY - JOUR AU - Gzyl, Henryk TI - On Poisson-Dirichlet problems with polynomial data JO - Publicacions Matemàtiques PY - 2002 VL - 46 IS - 2 SP - 465 EP - 471 AB - 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. LA - eng KW - Ecuaciones diferenciales estocásticas; Integración estocástica; Problemas de valor de frontera; Problema de Dirichlet; Ecuación de Poisson; Funciones polinómicas; Poisson-Dirichlet problems; stochastic calculus UR - http://eudml.org/doc/41460 ER -