A gårding's inequality for variational problems with constraints

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.

Keywords:

• Gårding's inequality
• constrained variational problems
• Fredholm alternative
• nonconforming Galerkin scheme
• Asymptotic convergence

Additional information

Notes on contributors

Gabriel N. Gatica