Isometric Immersion of Surface with Negative Gauss Curvature and the Lax--Friedrichs Scheme

DOI10.1137/15M1041766zbMath1341.53088arXiv1509.08584OpenAlexW2227267455WikidataQ125941265 ScholiaQ125941265MaRDI QIDQ2814478

Dehua Wang, Wentao Cao, Fei-Min Huang

Publication date: 22 June 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.08584

zbMATH Keywords

compensated compactnessLax-Friedrichs schemeisometric immersionGauss-Codazzi equationsuniform estimate\(L^\infty\) large solution

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) PDEs of mixed type (35M10) Hyperbolic conservation laws (35L65) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems on manifolds (58J32) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

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On the existence of \(C^{1,1}\)-isometric immersions of several classes of negatively curved surfaces into \(\mathbb{R}^3\)

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