The geometry of a singular set of hypersurfaces and the eikonal equation

DOI10.1134/S0001434620090114zbMath1451.35060OpenAlexW3096664061MaRDI QIDQ2210387

I. G. Tsar'kov

Publication date: 6 November 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434620090114

zbMATH Keywords

regular pointsun point

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (6)

Geometry of the singular set of hypersurfaces and the eikonal equation ⋮ Suns, moons, and \(\mathring{B}\)-complete sets in asymmetric spaces ⋮ Monotone path-connectedness of strict suns ⋮ Smoothness of solutions of the eikonal equation and regular points of their level surfaces ⋮ Solarity of Chebyshev sets in dual spaces and uniquely remotal sets ⋮ Ball-complete sets and solar properties of sets in asymmetric spaces

Cites Work

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• Connectedness and other geometric properties of suns and Chebyshev sets
• Singular sets of surfaces
• Necessary conditions for differentiability of distance functions
• Singularities of solutions of the eikonal equation
• Properties of \(C^1\)-solutions to the eikonal equation
• Connectedness and solarity in problems of best and near-best approximation
• GENERALIZED SOLUTIONS OF THE HAMILTON-JACOBI EQUATIONS OF EIKONAL TYPE. I. FORMULATION OF THE PROBLEMS; EXISTENCE, UNIQUENESS AND STABILITY THEOREMS; SOME PROPERTIES OF THE SOLUTIONS
• Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function

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