The distance function in the presence of an obstacle

DOI10.1007/s00526-021-02125-zOpenAlexW4206183622WikidataQ114228989 ScholiaQ114228989MaRDI QIDQ2062976

Paolo Albano, Vincenzo Basco, Piermarco Cannarsa

Publication date: 3 January 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.14960

Mathematics Subject Classification ID

Fixed-point theorems on manifolds (58C30) Convexity of real functions of several variables, generalizations (26B25)

Related Items (1)

On the regularity of the distance near the boundary of an obstacle

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Global propagation of singularities for solutions of Hamilton-Jacobi equations
• Long-time behavior of first-order mean field games on Euclidean space
• Singular dynamics for semiconcave functions
• On the local semiconcavity of the solutions of the eikonal equation
• On p-convex sets and geodesics
• Propagation of singularities for solutions of nonlinear first order partial differential equations
• Generalized characteristics and Lax-Oleinik operators: global theory
• Some properties of semiconcave functions with general modulus
• Singular gradient flow of the distance function and homotopy equivalence
• Unbounded components of the singular set of the distance function in $\mathbb R^n$
• Regularity of the Eikonal Equation with Neumann Boundary Conditions in the Plane: Application to Fronts with Nonlocal Terms
• Hamilton-Jacobi Equations with State Constraints
• Notions of convexity
• Riemannian geometry
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