Loss of regularity for Kolmogorov equations

Hölder Regularity for a Kolmogorov Equation

We study the interior regularity properties of the solutions to the degenerate parabolic equation, ∆xu+ b∂yu− ∂tu = f, (x, y, t) ∈ R × R× R, which arises in mathematical finance and in the theory of diffusion processes.

Kolmogorov Equations in Infinite Dimensions: Well-posedness and Regularity of Solutions, with Applications to Stochastic Generalized Burgers Equations

Abstract. We develop a new method to uniquely solve a large class of heat equations, so called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. This way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly no...

Martingale problems for some degenerate Kolmogorov equations

We obtain Calderón-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous nonlinear coefficients. We then derive the well-posedness of the martingale problem associated with related degenerate operators, and therefore uniqueness in law for the corresponding stochastic differential equations. Some density estimates are established as well.

Maximal Regularity for Evolution Equations

Loss of Gevrey Regularity for Asymptotic Optics

In this paper we will investigate some aspects of the asymptotic behavior of oscillatory integrals from the Gevrey point of view. We will give formal asymptotic expansions and study the Gevrey character of oscillatory integrals, in comparison with the Gevrey character of their amplitudes. We will deduce a formula for the loss of Gevrey regularity both for phase functions in the Morse class and ...