G. Prato

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math.PR2007★ 1 cited

Existence of Strong Solutions for Stochastic Porous Media Equation under General Monotonicity Conditions

Viorel Barbu, Giuseppe Da Prato, Michael Röckner

One proves existence and uniqueness of strong solutions to stochastic porous media equations under minimal monotonicity conditions on the nonlinearity. In particular, we do not ass…

math.PR2007★ 1 cited

Existence and Uniqueness of Nonnegative Solutions to the Stochastic Porous Media Equation

Viorel Barbu, Giuseppe Da Prato, Michael Röckner

One proves that the stochastic porous media equation in 3-D has a unique nonnegative solution for nonnegative initial data in $H^{- 1} (O)$ if the nonlinearity is monotone a…

math.PR2005

Gradient Bounds for Solutions of Elliptic and Parabolic Equations

Vladimir I. Bogachev, Giuseppe Da Prato, Michael Röckner +1

Let $L$ be a second order elliptic operator on $R^{d}$ with a constant diffusion matrix and a dissipative (in a weak sense) drift $b \in L_{l oc}^{p}$ with some $p > d$ . We assume that $L…