# Journal article

## Discontinuous solutions for Hamilton-Jacobi equations: Uniqueness and regularity

Abstract:

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 ...

### Access Document

Publisher copy:
10.3934/dcds.2003.9.167

### Authors

Journal:
Discrete and Continuous Dynamical Systems
Volume:
9
Issue:
1
Pages:
167-192
Publication date:
2003-01-01
DOI:
ISSN:
1078-0947
Language:
English
Keywords:
Pubs id:
pubs:203212
UUID:
uuid:c6260dec-704f-4d7c-9000-d0172c8bfd8a
Local pid:
pubs:203212
Source identifiers:
203212
Deposit date:
2012-12-19