A surface in \(W^{2,p}\) is a locally Lipschitz-continuous function of its fundamental forms in \(W^{1,p}\) and \(L^p\), \(p>2\)
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Publication:1732999
DOI10.1016/j.matpur.2018.06.013zbMath1411.53008OpenAlexW4321428007MaRDI QIDQ1732999
Philippe G. Ciarlet, Christinel Mardare
Publication date: 26 March 2019
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matpur.2018.06.013
Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Surfaces in Euclidean and related spaces (53A05)
Related Items (5)
Asymptotic rigidity for shells in non-Euclidean elasticity ⋮ On asymptotic rigidity and continuity problems in nonlinear elasticity on manifolds and hypersurfaces ⋮ Stability of isometric immersions of hypersurfaces ⋮ Continuity in Fréchet topologies of a surface as a function of its fundamental forms ⋮ Continuity of a surface in Fréchet spaces
Cites Work
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- On systems of first order linear partial differential equations with \(L^p\) coefficients
- The continuity of a surface as a function of its two fundamental forms.
- \(W^{2,p}\)-estimates for surfaces in terms of their two fundamental forms
- Recovery of a manifold with boundary and its continuity as a function of its metric tensor
- On Pfaff systems with \(L^p\) coefficients and their applications in differential geometry
- RECOVERY OF A SURFACE WITH BOUNDARY AND ITS CONTINUITY AS A FUNCTION OF ITS TWO FUNDAMENTAL FORMS
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