@inproceedings{ConstalesKrausshar,
author = {Constales, Denis and Kraußhar, Rolf S{\"o}ren},
title = {ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS},
editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
organization = {Bauhaus-Universit{\"a}t Weimar},
issn = {1611-4086},
doi = {10.25643/bauhaus-universitaet.2863},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28639},
pages = {10},
abstract = {In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.},
subject = {Angewandte Informatik},
language = {en}
}
@inproceedings{CacaoConstalesKrausshar,
author = {Cacao, Isabel and Constales, Denis and Kraußhar, Rolf S{\"o}ren},
title = {A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES},
editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
organization = {Bauhaus-Universit{\"a}t Weimar},
issn = {1611-4086},
doi = {10.25643/bauhaus-universitaet.2834},
url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-28343},
pages = {8},
abstract = {Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.},
subject = {Angewandte Informatik},
language = {en}
}