We consider a multidimensional Burgers equation on the torus T and the whole space R . We show that, in case of the torus, there exists a unique global solution in Lebesgue spaces. For a torus we… (More)

We study a class of optimal control problems with state constraints, where the state equation is a differential equation with delays. This class includes some problems arising in economics, in… (More)

This paper, which is the natural continuation of [14], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. In [14] the… (More)

We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in… (More)

We extend the proof of the dynamic programming principle (DPP) for standard stochastic optimal control problems driven by general Lévy noise. Under appropriate assumptions, it is shown that the DPP… (More)

This paper, which is the natural continuation of [21], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class… (More)

We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in… (More)

We consider convex functions on infinite dimensional spaces equipped with measures. Our main results give some estimates of the first and second derivatives of a convex function, where second… (More)

Let H be a separable Hilbert space and let A : D(A) ⊂ H → H be a selfadjoint operator with A ≤ ωI, ω > 0 and Tr ( −A−1 ) <∞. We endow H with the centered Gaussian measure μ with covariance operator Q… (More)