Kernel estimates for nonautonomous Kolmogorov equations

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients

Analytic approach to solve a degenerate parabolic PDE for the Heston Model

We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half-plane

On vector-valued Schrödinger operators with unbounded diffusion in Lp spaces

We prove generation results of analytic strongly continuous semigroups on Lp(Rd, Rm) (1 < p< ∞) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups

On the chaotic behaviour of size structured cell populations

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Instantaneous blowup and singular potentials on Heisenberg groups

In this paper we generalize the instantaneous blowup result from [3] and [15] to the heat equation perturbed by singular potentials on the Heisenberg group

LpL^p-regularity for elliptic operators with unbounded coefficients

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