Coerciveness Inequality for Nonlocal Boundary value Problems for Second Order Abstract Elliptic Differential Equations

Volume 4, Issue 2, 2003

Article 43

COERCIVENESS INEQUALITY FOR NONLOCAL BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ABSTRACT ELLIPTIC DIFFERENTIAL EQUATIONS

AISSA AIBECHE

DEPARTMENT OF MATHEMATICS,
FACULTY OF SCIENCES
UNIVERSITY FERHAT ABBAS,
ROUTE DE SCIPION, 19000,
SETIF, ALGERIA.
E-Mail: aibeche@wissal.dz

Received 09 December, 2002; Accepted 17 March, 2003.
Communicated by: Z. Nashed

ABSTRACT. In this paper we give conditions which assure the coercive solvability of an abstract differential equation of elliptic type with an operator in the boundary conditions, and the completeness of generalized eigen functions. We apply the abstract result to show that a non regular boundary value problem for a second order partial differential equation of an elliptic type in a cylindrical domain is coercive solvable.

Key words:
Ellipticity, Abstract Differential Equation, Coerciveness, Non Regular Elliptic Problems.

2000 Mathematics Subject Classification:
35J05, 35P20, 34L10, 47E05.

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