New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization.

• Bouarroudj, Nadra ^[2] ; Belaib, Lekhmissi ^[1] ; Messirdi, Bekkai ^[3]
  1. [1] University of Oran

     University of Oran

     Argelia

     
  2. [2] ENP Oran Maurice Audin.
  3. [3] Laboratory of Fundamental and Applicable Mathematics of Oran .

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 4, 2018, págs. 749-764
• Idioma: inglés
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• Resumen

  • The method of invariant embedding for the solutions of boundary value problems yields an equivalent formulation to the initial boundary value problems by a system of Riccati operator differential equations. A combined technique based on invariant embedding approach and Yosida regularization is proposed in this paper for solving abstract Riccati problems and Dirichlet problems for the Poisson equation over a circular domain. We exhibit, in polar coordinates, the associated Neumann to Dirichlet operator, somme concrete properties of this operator are given. It also comes that from the existence of a solution for the corresponding Riccati equation, the problem can be solved in appropriate Sobolev spaces.