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

Alexandre Ern
, Jean Luc Guermond

Texas A&M University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Translated title of the contribution	Une réciproque au lemme de Fortin dans les espaces de Banach
Original language	English
Pages (from-to)	1092-1095
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	11
DOIs	https://doi.org/10.1016/j.crma.2016.09.013
Publication status	Published - 1 Nov 2016

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title = "A converse to Fortin's Lemma in Banach spaces",

abstract = "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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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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DO - 10.1016/j.crma.2016.09.013

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AN - SCOPUS:84994065805

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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A converse to Fortin's Lemma in Banach spaces

Abstract

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