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The hyperbolic dirichlet problem

Authors
Journal
Mathematical and Computer Modelling
0895-7177
Publisher
Elsevier
Publication Date
Volume
32
Identifiers
DOI: 10.1016/s0895-7177(00)00137-0
Keywords
  • Transitive Curve
  • Hyperbolic Dirichlet Problem
  • Rotation Number
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract The aim of this paper is to take into account the hyperbolic Dirichlet problem on a given transitive curve of the plane. Owing to a representation theorem, we can assume without loss of generality, that our curve is an ellipse. Therefore, given an ellipse and a smooth function on its boundary, we show that there are uncountably many rotations which assure existence and unicity for the corresponding solution of the hyperbolic Dirichlet problem. Moreover, we give a numerical algorithm for the effective computation of the solution.

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