A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet

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We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup $P_{t} φ$ does exist for any bounded $φ$ ; and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given.

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