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On the exterior two-dimensional Dirichlet problem for elliptic equations

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Abstract

A necessary and sufficient condition is given on the boundary datum in order to the Dirichlet problem for an elliptic equation in a two-dimensional exterior Lipschitz domain has a unique solution with a finite Dirichlet integral which converges uniformly at infinity to an assigned constant value.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università di, NapoliviaVivaldi 43, I81100, Caserta, Italy

    Remigio Russo

  2. Department of Mathematics, University of Bayreuth, 95440, Bayreuth, Germany

    Christian G. Simader

Authors
  1. Remigio Russo
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  2. Christian G. Simader
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Correspondence to Remigio Russo.

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Russo, R., Simader, C.G. On the exterior two-dimensional Dirichlet problem for elliptic equations. Ricerche mat. 58, 315–328 (2009). https://doi.org/10.1007/s11587-009-0066-9

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  • DOI: https://doi.org/10.1007/s11587-009-0066-9

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