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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Submitted on : Wednesday, June 22, 2016 - 12:45:02 PM
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Alexandre Ern, Jean-Luc Guermond. A converse to Fortin's Lemma in Banach spaces. Comptes Rendus Mathématique, Elsevier Masson, 2016, 354 (11), pp.1092-1095. ⟨10.1016/j.crma.2016.09.013⟩. ⟨hal-01273901v2⟩

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