Laplace type operators: Dirichlet problem

Wojciech Kozł

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

  • Volume: 6, Issue: 1, page 53-80
  • ISSN: 0391-173X

Abstract

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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 𝖲𝖮 ( n ) -irreducible subspaces.

How to cite

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Kozł, Wojciech. "Laplace type operators: Dirichlet problem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.1 (2007): 53-80. <http://eudml.org/doc/272295>.

@article{Kozł2007,
abstract = {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 $\mathsf \{SO\}(n)$-irreducible subspaces.},
author = {Kozł, Wojciech},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Laplace type operator; Dirichlet boundary value problem; existence of solutions},
language = {eng},
number = {1},
pages = {53-80},
publisher = {Scuola Normale Superiore, Pisa},
title = {Laplace type operators: Dirichlet problem},
url = {http://eudml.org/doc/272295},
volume = {6},
year = {2007},
}

TY - JOUR
AU - Kozł, Wojciech
TI - Laplace type operators: Dirichlet problem
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2007
PB - Scuola Normale Superiore, Pisa
VL - 6
IS - 1
SP - 53
EP - 80
AB - 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 $\mathsf {SO}(n)$-irreducible subspaces.
LA - eng
KW - Laplace type operator; Dirichlet boundary value problem; existence of solutions
UR - http://eudml.org/doc/272295
ER -

References

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  12. [12] E. M. Stein and G. Weiss, “Fourier Analysis on Euclidean Spaces”, Princeton University Press, 1971. Zbl0232.42007MR304972
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