Proximal analysis and the minimal time function

Peter R. Wolenski, Yu Zhuang

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


Under general hypotheses on the target set S and the dynamics of the system, we show that the minimal time function TS(·) is a proximal solution to the Hamilton-Jacobi equation. Uniqueness results are obtained with two different kinds of boundary conditions. A new propagation result is proven, and as an application, we give necessary and sufficient conditions for TS(·) to be Lipschitz continuous near S. A Petrov-type modulus condition is also shown to be sufficient for continuity of TS(·) near S.

Original languageEnglish
Pages (from-to)1048-1072
Number of pages25
JournalSIAM Journal on Control and Optimization
Issue number3
StatePublished - 1998


  • Continuity of value functions
  • Hamilton-Jacobi equations
  • Minimal time function
  • Nonsmooth analysis
  • Proximal analysis


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