ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS

Constales, Denis; Kraußhar, Rolf Sören

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.

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Constales, Denis / Kraußhar, Rolf Sören: ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS. 2010.

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