Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function

DOI10.1070/IM8850zbMath1429.41034OpenAlexW2954501150WikidataQ127624320 ScholiaQ127624320MaRDI QIDQ5207132

I. G. Tsar'kov

Publication date: 7 January 2020

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8850

zbMATH Keywords

eikonal equationcausticregular setssingular setssolarity points

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Geometric optics (78A05)

Related Items (6)

Geometry of the singular set of hypersurfaces and the eikonal equation ⋮ Smoothness of subspace sections of the unit balls of \(C(Q)\) and \(L^1\) ⋮ Smoothness of solutions of the eikonal equation and regular points of their level surfaces ⋮ Strict protosuns in asymmetric spaces of continuous functions ⋮ Characterization of sets with continuous metric projection in the space \(\ell^\infty_n\) ⋮ The geometry of a singular set of hypersurfaces and the eikonal equation

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
• 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
• Fixed Point Theorems for Multi-Valued Transformations

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