Publication Cover
Applicable Analysis
An International Journal
Volume 54, 1994 - Issue 1-2
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Original Articles

A gårding's inequality for variational problems with constraints

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Pages 73-90 | Received 02 Oct 1992, Published online: 02 May 2007
 

Abstract

In this paper we introduce a generalization of the usual Gårding inequality for bounded bilinear forms defined on Hilbert spaces. In addition, we give sufficient conditions for a variational problem with constraints to satisfy this generalized inequality, and show that this result induces a new procedure for the numerical treatment of such problems. More precisely, we prove that if a constrained variational problem is uniquely solvable and if its associated biliear form satisfies the generalized Gårding inequality then an asymptotically convergent nonconforming Galerkin scheme for approximating the continuous solution can be derived.

Additional information

Notes on contributors

Gabriel N. Gatica

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