A converse to Fortin's Lemma in Banach spaces

Alexandre Ern; Jean Luc Guermond

doi:10.1016/j.crma.2016.09.013

A converse to Fortin's Lemma in Banach spaces

Titre traduit de la contribution: Une réciproque au lemme de Fortin dans les espaces de Banach

Alexandre Ern
, Jean Luc Guermond

Texas A&M University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We establish the converse of Fortin's Lemma in Banach spaces. This result is useful to assert the existence of a Fortin operator once a discrete inf–sup condition has been proved. The proof uses a specific construction of a right-inverse of a surjective operator in Banach spaces. The key issue is the sharp determination of the stability constants.

Titre traduit de la contribution	Une réciproque au lemme de Fortin dans les espaces de Banach
langue originale	Anglais
Pages (de - à)	1092-1095
Nombre de pages	4
journal	Comptes Rendus Mathematique
Volume	354
Numéro de publication	11
Les DOIs	https://doi.org/10.1016/j.crma.2016.09.013
état	Publié - 1 nov. 2016

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10.1016/j.crma.2016.09.013

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AB - We establish the converse of Fortin's Lemma in Banach spaces. This result is useful to assert the existence of a Fortin operator once a discrete inf–sup condition has been proved. The proof uses a specific construction of a right-inverse of a surjective operator in Banach spaces. The key issue is the sharp determination of the stability constants.

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A converse to Fortin's Lemma in Banach spaces

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