On Dirichlet’s Boundary Value Problem for Certain Anisotropic Differential and Pseudo-Differential Operators

Karl Doppel and Niels Jacob
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Karl Doppel: FU Berlin
Niels Jacob: FAU Erlangen

A chapter in Potential Theory, 1988, pp 75-83 from Springer

Abstract: Abstract In our previous paper [1] a calculus for pseudo-differential operators was used to find periodic solutions for a large class of not necessarily elliptic pseudo-differential equations with constant coefficients. In this paper we consider a generalized homogeneous Dirichlet-problem for pseudo — differential operators with constant coefficients and prove Fredholm’s alternative theorem. We give two examples how to apply this result. The first one is a differential operator arising in stochastics. In the second example we deal with an anisotropic pseudo-differential operator and using the theory of Dirichlet forms (see [4]) it follows that this operator generates a symmetric Hunt process. Some of our results had been already used in [6].

Keywords: Periodic Solution; Constant Coefficient; Dirichlet Form; Continuous Extension; Aequationes Math (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-0981-9_11

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DOI: 10.1007/978-1-4613-0981-9_11

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