L²-data Dirichlet problem for weighted form Laplacians
We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.
La méthode de Fourier pour des équations abstraites
Laurent series expansion for solutions of hypoelliptic equations
We prove that any zero solution of a hypoelliptic partial differential operator can be expanded in a generalized Laurent series near a point singularity if and only if the operator is semielliptic. Moreover, the coefficients may be calculated by means of a Cauchy integral type formula. In particular, we obtain explicit expansions for the solutions of the heat equation near a point singularity. To prove the necessity of semiellipticity, we additionally assume that the index of hypoellipticity with...
Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques
Le problème de Cauchy ramifié linéaire pour des données à singularités algébriques
Liouville theorem for Dunkl polyharmonic functions.