Newton's method in constructing a singular set of a minimax solution in a class of boundary value problems for the Hamilton-Jacobi equations

DOI10.47475/2500-0101-2024-9-1-63-76MaRDI QIDQ6497130

A. A. Uspenskii, Pavel Dmitrievich Lebedev

Publication date: 6 May 2024

Published in: Chelyabinskiĭ Fiziko-Matematicheskiĭ Zhurnal (Search for Journal in Brave)

zbMATH Keywords

diffeomorphismHamilton-Jacobi equationwave frontspeedminimax solutionsingular seteikonalpseudovertex

Mathematics Subject Classification ID

Mechanics of deformable solids (74-XX) Numerical analysis (65-XX)

Cites Work

• Connectedness and solarity in problems of best and near-best approximation
• Viscosity Solutions of Hamilton-Jacobi Equations
• 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
• Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set
• On singularity structure of minimax solution to Dirichlet problem for eikonal type equation with discontinuous curvature of boundary of boundary set
• Construction of a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary
• Alpha-sets in finite dimensional Euclidean spaces and their properties
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