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Search: All articles in the CJM digital archive with keyword elliptic operator

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1. CJM 2002 (vol 54 pp. 1280)

Skrzypczak, Leszek
Besov Spaces and Hausdorff Dimension For Some Carnot-Carathéodory Metric Spaces
We regard a system of left invariant vector fields $\mathcal{X}=\{X_1,\dots,X_k\}$ satisfying the H\"ormander condition and the related Carnot-Carath\'eodory metric on a unimodular Lie group $G$. We define Besov spaces corresponding to the sub-Laplacian $\Delta=\sum X_i^2$ both with positive and negative smoothness. The atomic decomposition of the spaces is given. In consequence we get the distributional characterization of the Hausdorff dimension of Borel subsets with the Haar measure zero.

Keywords:Besov spaces, sub-elliptic operators, Carnot-Carathéodory metric, Hausdorff dimension
Categories:46E35, 43A15, 28A78

2. CJM 2002 (vol 54 pp. 945)

Boivin, André; Gauthier, Paul M.; Paramonov, Petr V.
Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications
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
Categories:30D40, 30E10, 31B35, 35Jxx, 35J67, 41A30

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