Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 478, Issue 2, Pages 990-1004Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.06.002
Keywords
Laplace transformation; Vector-valued distributions; Poly- and rnetaharmonic operator; Dirichlet problem in half spaces; Poisson kernels; Iterated wave- and Klein-Gordon operators
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Funding
- Austrian Science Fund FWF [P26859, P30233]
- Austrian Science Fund (FWF) [P26859, P30233] Funding Source: Austrian Science Fund (FWF)
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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.
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