location:  Publications → journals → CJM
Abstract view

# Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications

Published:2002-10-01
Printed: Oct 2002
• André Boivin
• Paul M. Gauthier
• Petr V. Paramonov
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Given 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 $\Omega$ in $\mathbf{R}^n$ 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.
 Keywords: approximation on closed sets, elliptic operator, strongly elliptic operator, $L$-meromorphic and $L$-analytic functions, localization operator, Banach space of distributions, Dirichlet problem
 MSC Classifications: 30D40 - Cluster sets, prime ends, boundary behavior 30E10 - Approximation in the complex domain 31B35 - Connections with differential equations 35Jxx - Elliptic equations and systems [See also 58J10, 58J20] 35J67 - Boundary values of solutions to elliptic equations 41A30 - Approximation by other special function classes

 top of page | contact us | privacy | site map |