Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Benedict Baur
University of Kaiserslautern
Strong Feller Property up to the Boundary for Elliptic Diffusions
For a gradient Dirichlet form with Hölder continuous matrix and density and a piecewise C 1 -domain we
prove L p -strong Feller property of the associated resolvent and semigroup. Under additional smoothness
assumptions on the coefficients and the boundary we construct a diffusion process with generalized reflection
at the boundary starting in all points where the density is not zero and which are either interior
points or have local C 2 -smooth boundary. Finally we apply these concepts to the construction of stochastic
dynamics for interacting particle systems.
Literatur
S. V. Shaposhnikov, On Morrey’s Estimate of Solutions of Elliptic Equations.
V. I. Bogachev, N. V. Krylov, M. Röckner. On Regularity of Transition Probabilities and Invariant Measures
of Singular Diffusions under minimal conditions. Communications in Partial Differential Equations, 26(11-
12):2037-2080, 2001.
S. Albeverio, Yu. G. Kondratiev and M. Röckner. Strong Feller properties for distorted Brownian motion
and applications to finite particle systems with singular interactions. In Infinite Dimensional Analysis in
Honor of Leonard Gross, volume 317 of Contemporary Mathematics. Amer. Math. Soc., Providence, RI,
2003.
T. Fattler and M. Grothaus. Strong Feller property for distorted Brownian motion with reflecting bounday
condition. Journal of Functional Analysis, 246(2): 217-241. 2007
Christoph Berns
Universität Bielefeld
Kawasaki Dynamics of Continuous Interacting Particle Systems
In this talk we discuss a stochastic (conservative) jump dynamics of interacting particles in continuum.
This dynamics is an analog of the Kawasaki dynamics of lattice spin systems. The Kawasaki dynamics is
now process where interacting particles randomly hop over R d . We give a microscopic and a mesoscopic
description of such dynamics.
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