Discontinuous solutions for Hamilton-Jacobi equations: Uniqueness and regularity

Journal article

The uniqueness of classical semicontinuous viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with convex Hamiltonians H = H (Du) is established, provided the discontinuous initial value function φ(x) is continuous outside a set Γ of measure zero and satisfies φ(x) ≥ φ**(x) ≡ liminfy→x,y∈ℝd\Γ φ (y). The regularity of discontinuous solutions to Hamilton-Jacobi equations with locally strictly convex Hamiltonians is proved: The discontinuous solutions with almost everywhere ...

Expand abstract

Authors: Chen, G; Su, B

• Journal: Discrete and Continuous Dynamical Systems
• Volume: 9
• Issue: 1
• Pages: 167-192
• Publication date: 2003-01-01
• DOI: 10.3934/dcds.2003.9.167
• ISSN: 1078-0947
• Language: English
• Keywords: Viscosity solutions; Semicontinuous solutions; Minimax solutions; Stability; Hamilton-Jacobi equations; Regularity after finite time; Accessibility of initial data; L∞ solutions; Discontinuous solutions