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://www.numdam.org/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://www.numdam.org/item/ASNSP_2007_5_6_1_53_0/ LA - en ID - ASNSP_2007_5_6_1_53_0 ER -
Kozł, Wojciech. Laplace type operators: Dirichlet problem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, pp. 53-80. http://www.numdam.org/item/ASNSP_2007_5_6_1_53_0/
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