Viscosity Solutions of the Eikonal Equation on the Wasserstein Space

H. Mete Soner, Qinxin Yan

Research output: Contribution to journalArticlepeer-review


Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity theory. We use Fourier representation of the Sobolev norms on the space of measures, together with the standard techniques from the finite dimensional theory to prove a comparison result among semi-continuous sub and super solutions, obtaining a unique characterization of the value function.

Original languageEnglish (US)
Article number1
JournalApplied Mathematics and Optimization
Issue number1
StatePublished - Aug 2024

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • 35D40
  • 35Q89
  • 49L25
  • 60G99
  • Eikonal Equation
  • Mean Field Games
  • Mean-field control
  • Viscosity Solutions
  • Wasserstein space


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