On the local semiconcavity of the solutions of the eikonal equation

DOI10.1016/j.na.2010.03.038zbMath1192.35033OpenAlexW2016675040MaRDI QIDQ975845

Paolo Albano

Publication date: 11 June 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.03.038

zbMATH Keywords

locally semiconvex Hamiltonian

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Nonlinear first-order PDEs (35F20) Viscosity solutions to PDEs (35D40)

Related Items (11)

On the stability of the cut locus ⋮ On the Subelliptic Eikonal Equation ⋮ The regularity of the distance function propagates along minimizing geodesics ⋮ Regularity results for the minimum time function with Hörmander vector fields ⋮ On the extension of the solutions of Hamilton-Jacobi equations ⋮ Equivalence of solutions of eikonal equation in metric spaces ⋮ On the Eikonal equation for degenerate elliptic operators ⋮ On the cut locus of closed sets ⋮ Global propagation of singularities for solutions of Hamilton-Jacobi equations ⋮ The distance function in the presence of an obstacle ⋮ On the regularity of the distance near the boundary of an obstacle

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Viscosity solutions of Hamilton-Jacobi equations
• Propagation of singularities for solutions of nonlinear first order partial differential equations
• On the singularities of convex functions
• Some properties of semiconcave functions with general modulus
• A Simple, Direct Proof of Uniqueness for Solutions of the Hamilton-Jacobi Equations of Eikonal Type
• Some Characterizations of Optimal Trajectories in Control Theory
• Semiconcavity of solutions of stationary Hamilton-Jacobi equations
• Representation formulas for solutions of Hamilton-Jacobi equations with convex Hamiltonians
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