Geodesic
Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 267-277

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider a stochastic Burgers equation. We show that the gradient of the corresponding transition semigroup \( P_{t} \varphi \) does exist for any bounded \( \varphi \); and can be estimated by a suitable exponential weight. An application to some Hamilton-Jacobi equation arising in Stochastic Control is given. 
@article{RLIN_1998_9_9_4_a3,
     author = {Da Prato, Giuseppe and Debussche, Arnaud},
     title = {Differentiability of the transition semigroup of the stochastic {Burgers} equation, and application to the corresponding {Hamilton-Jacobi} equation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {267--277},
     publisher = {mathdoc},
     volume = {Ser. 9, 9},
     number = {4},
     year = {1998},
     zbl = {0931.37036},
     mrnumber = {MR1722786},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a3/}
}
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Da Prato, Giuseppe; Debussche, Arnaud. Differentiability of the transition semigroup of the stochastic Burgers equation, and application to the corresponding Hamilton-Jacobi equation. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 267-277. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a3/