Abstract
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.
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Lasry, J.M., Lions, P.L. A remark on regularization in Hilbert spaces. Israel J. Math. 55, 257–266 (1986). https://doi.org/10.1007/BF02765025
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DOI: https://doi.org/10.1007/BF02765025