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We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into -irreducible subspaces.
@article{ASNSP_2007_5_6_1_53_0,
author = {Koz{\l}, Wojciech},
title = {Laplace type operators: {Dirichlet} problem},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {53--80},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {1},
year = {2007},
mrnumber = {2341515},
zbl = {1185.35039},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_53_0/}
}
TY - JOUR AU - Kozł, Wojciech TI - Laplace type operators: Dirichlet problem JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 53 EP - 80 VL - 6 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_53_0/ LA - en ID - ASNSP_2007_5_6_1_53_0 ER -
%0 Journal Article %A Kozł, Wojciech %T Laplace type operators: Dirichlet problem %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 53-80 %V 6 %N 1 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_53_0/ %G en %F ASNSP_2007_5_6_1_53_0
Kozł, Wojciech. Laplace type operators: Dirichlet problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 1, pp. 53-80. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_1_53_0/