Laplace type operators: Dirichlet problem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 1, p. 53-80

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 𝖲𝖮(n)-irreducible subspaces.

Classification:  35J25,  34K10,  35J67
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {1},
     year = {2007},
     pages = {53-80},
     zbl = {1185.35039},
     mrnumber = {2341515},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_1_53_0}
}
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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