Author:
Boivin André,Gauthier Paul M.,Paramonov Petr V.
Abstract
AbstractGiven a homogeneous elliptic partial differential operator L with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain Ω in Rn and which belong locally to a Banach space V, we consider the problem of approximating in the norm of V the functions in this class by “analytic” and “meromorphic” solutions of the equation Lu = 0. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces V and operators L. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.
Publisher
Canadian Mathematical Society
Cited by
12 articles.
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