Laplace transformation of vector-valued distributions and applications to Cauchy-Dirichlet problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Kunzinger, Michael¹  Nigsch, Eduard A.¹  Ortner, Norbert² 

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Univ Innsbruck, Dept Math, Tech Str 13, A-6020 Innsbruck, Austria

关键词: Laplace transformation;    Vector-valued distributions;    Poly- and rnetaharmonic operator;    Dirichlet problem in half spaces;    Poisson kernels;    Iterated wave- and Klein-Gordon operators;   

DOI  :  10.1016/j.jmaa.2019.06.002

来源: Elsevier

【 摘 要 】

We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain explicit solutions to Cauchy-Dirichlet problems of iterated wave- and Klein-Gordon operators in half-spaces. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free