Israel Journal of Mathematics

, Volume 55, Issue 3, pp 257-266

First online:

A remark on regularization in Hilbert spaces

  • J. M. LasryAffiliated withCeremade, Université Paris - Dauphine
  • , P. L. LionsAffiliated withCeremade, Université Paris - Dauphine

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We present here a simple method to approximate uniformly in Hilbert spaces uniformly continuous functions byC 1,1 functions. This method relies on explicit inf-sup-convolution formulas or equivalently on the solutions of Hamilton-Jacobi equations.