\(W^{2,p}\)-estimates for surfaces in terms of their two fundamental forms

DOI10.1016/j.crma.2017.12.003zbMath1390.53007OpenAlexW2776910504MaRDI QIDQ1704651

Philippe G. Ciarlet, Christinel Mardare

Publication date: 12 March 2018

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2017.12.003

zbMATH Keywords

nonlinear Korn inequalitysimply-connected open subset

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Methods of local Riemannian geometry (53B21)

Related Items (2)

Continuity in Fréchet topologies of a surface as a function of its fundamental forms ⋮ A surface in \(W^{2,p}\) is a locally Lipschitz-continuous function of its fundamental forms in \(W^{1,p}\) and \(L^p\), \(p>2\)

Cites Work

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• Nonlinear Korn inequalities in \(\mathbb R^n\) and immersions in \(W^{2,p}\), \(p>n\), considered as functions of their metric tensors in \(W^{1,p}\)
• On systems of first order linear partial differential equations with \(L^p\) coefficients
• On Pfaff systems with \(L^p\) coefficients and their applications in differential geometry

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