BV weak solutions to Gauss-Codazzi system for isometric immersions

DOI10.1016/j.jde.2011.08.046zbMath1231.53053OpenAlexW2010967979WikidataQ60117393 ScholiaQ60117393MaRDI QIDQ656190

Cleopatra C. Christoforou

Publication date: 16 January 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.08.046

zbMATH Keywords

bounded variationGauss curvatureisometric immersion problemsystems of balance lawsrandom choice methodfirst and second fundamental forms

Mathematics Subject Classification ID

Transonic flows (76H05) 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) Initial value problems for first-order hyperbolic systems (35L45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45)

Related Items (9)

On Hyperbolic Balance Laws and Applications ⋮ On the decay rate of the Gauss curvature for isometric immersions ⋮ Isometric immersions of surfaces with two classes of metrics and negative Gauss curvature ⋮ Corrugated versus smooth uniqueness and stability of negatively curved isometric immersions ⋮ Isometric immersions via compensated compactness for slowly decaying negative Gauss curvature and rough data ⋮ Global BV entropy solutions to the Gauss-Codazzi system ⋮ Isometric Immersion of Surface with Negative Gauss Curvature and the Lax--Friedrichs Scheme ⋮ On the existence of \(C^{1,1}\)-isometric immersions of several classes of negatively curved surfaces into \(\mathbb{R}^3\) ⋮ The semi-global isometric embedding of surfaces with curvature changing signs stably

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