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Weak-Strong Uniqueness Principle for Hamilton-Jacobi Equations
- Publication Year :
- 2024
-
Abstract
- We show that if a Hamilton-Jacobi equation admits a differentiable solution whose gradient is Lipschitz, then this solution is the unique semi-concave weak solution. Our result does not rely on any convexity (nor concavity) assumptions on the initial condition or the nonlinearity, and can therefore be utilized in contexts where the viscosity solution admits no standard variational representation.<br />Comment: 13 pages
- Subjects :
- Mathematics - Analysis of PDEs
35F21, 35D30, 35D40
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2410.00628
- Document Type :
- Working Paper