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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 761–781
DOI: 10.4171/ZAA/1107

Published online: 2002-09-30

Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations

Gabriel N. Gatica[1]

(1) Universidad de Concepción, Chile

We generalize the usual Babuska-Brezzi theory to a class of nonlinear variational problems with constraints. The corresponding operator equation has a dual-dual type structure since the nonlinear operator involved has itself a dual structure with a strongly monotone and Lipschitz-continuous main operator. We provide sufficient conditions for the existence and uniqueness of solution of the continuous and Galerkin formulations, and derive a Strang-type estimate for the associated error. An application to the coupling of mixed-FEM and BEM for a nonlinear transmission problem in potential theory is also described.

Keywords: Dual-dual formulation of problems, extended Babuska-Brezzi theory, inf-sup conditions, strongly monotone operators

Gatica Gabriel: Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations. Z. Anal. Anwend. 21 (2002), 761-781. doi: 10.4171/ZAA/1107