Analytic Semigroups and Degenerate Elliptic Operators with Unbounded Coefficients: A Probabilistic Approach

Analytic Semigroups and Degenerate Elliptic Operators with Unbounded Coefficients: A Probabilistic Approach

In the present paper we are dealing with generation of analytic semigroups in the space of continuous and bounded functions by suitable second order differential operators, which have unbounded coefficients and may be degenerate. This means that we are away from the classical framework in the study of the generation of analytic semigroups by elliptic operators (see Lunardi [25] for a comprehens...

L^p-Regularity for Elliptic Operators with Unbounded Coefficients

Quantum dynamical semigroups generated by noncommutative unbounded elliptic operators

We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.

A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients

In this paper, we establish existence and uniqueness of solutions of a class of mixed boundary value problems for elliptic operators with singular coefficients. Our approach is probabilistic. The theory of Dirichlet forms plays an important role. AMS Subject Classification: Primary 60H15 Secondary 93E20, 35R60.

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Abstract. In this article, using DiPerna-Lions theory [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinea...