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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917


BOUARROUDJ, Nadra; BELAIB, Lekhmissi  y  MESSIRDI, Bekkai. New interpretation of elliptic Boundary value problems via invariant embedding approach and Yosida regularization. Proyecciones (Antofagasta) [online]. 2018, vol.37, n.4, pp.749-764. ISSN 0716-0917.

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.

Palabras clave : Elliptic boundary value problems; Invariant embedding method; Riccati operator differential equations; Yosida regularization; Neumann to Dirichlet operator.

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