Geodesic
H\"older estimates for solutions of parabolic SPDEs
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 152-159

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This paper considers second-order stochastic partial differential equations with additive noise given in a bounded domain of $R^n$. We suppose that the coefficients of the noise are $L^p$-functions with sufficiently large $p$. We prove that the solutions are Hölder-continuous functions almost surely (a.s.) and that the respective Hölder norms have finite momenta of any order.
Keywords: stochastic equation, Hölder-continuous function. 
@article{TVP_2002_47_1_a11,
     author = {S. B. Kuksin and N. S. Nadirashvili and A. L. Piatnitski},
     title = {H\"older estimates for solutions of parabolic {SPDEs}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {152--159},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a11/}
}
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S. B. Kuksin; N. S. Nadirashvili; A. L. Piatnitski. H\"older estimates for solutions of parabolic SPDEs. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 152-159. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a11/