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

In: Potential Theory

Author

Listed:
  • Karl Doppel

    (FU Berlin)

  • Niels Jacob

    (FAU Erlangen)

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].

Suggested Citation

  • Karl Doppel & Niels Jacob, 1988. "On Dirichlet’s Boundary Value Problem for Certain Anisotropic Differential and Pseudo-Differential Operators," Springer Books, in: Josef Král & Jaroslav Lukeš & Ivan Netuka & Jiří Veselý (ed.), Potential Theory, pages 75-83, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0981-9_11
    DOI: 10.1007/978-1-4613-0981-9_11
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