Wilhelm Stannat

Publications (2)0 Total impact

• Source

  Available from: ArXiv

  Article: Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow

  Abelhadi Es-Sarhir, Max von Renesse, Wilhelm Stannat
  [show abstract] [hide abstract]
  ABSTRACT: We establish moment estimates for the invariant measure of a stochastic partial differential equation describing motion by mean curvature flow in (1+1) dimension, leading to polynomial stability of the associated Markov semigroup. We also prove maximal dissipativity for the related Kolmogorov operator.
  08/2010;
• Article: Uniqueness of invariant measures and maximal dissipativity of diffusion operators on L¹

  Vladimir I. Bogachev, Michael Rckner, Universitt Bielefeld, Wilhelm Stannat
  [show abstract] [hide abstract]
  ABSTRACT: It is proved that there exists at most one probability measure on R d , so that L = 0, where L = a ij @ i @ j + b i @ i , provided L; C 1 0 (R) is maximally dissipative on L 1 (R d ; ) for at least one , so that L = 0. Here it is assumed that (a ij ) is non-degenerate, a ij 2 H p;1 loc , and b i 2 L p loc . We also present a whole class of examples (even for a ij = ij ), where L = 0 has more than one solution. Furthermore, recent related results are reviewed. subject classication: keywords and phrases: invariant measures, elliptic equations, second order partial dierential operators, maximal dissipativity, diusion operators, weighted Sobolev spaces running head: Invariant measures and maximal dissipativity. Contents 1 Introduction and framework 2 2 Survey of known results and some generalizations 3 2.1 Regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Existence . . . . . . . . . . . . . . . . . . ...
  02/1970;