Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0859.60071
Zheng, Weian
Meyer's topology and Brownian motion in a composite medium. (English)
[A] Azéma, J. (ed.) et al., Séminaire de probabilités XXX. Berlin: Springer. Lect. Notes Math. 1626, 108-116 (1996). ISBN 3-540-61336-6/pbk

A set $F$ in $\bbfR^d$ is said to have locally finite lower Minkowski content if $\liminf_{r\to 0}{1\over r}$ (the Lebesgue measure of $\{x: |x|< n, 0<\text{dis}(x,F)\le r\})$ is finite for each $n$. A heat propagation problem in a fixed composite medium, described by a finite number of open sets $A_i$ with different thermal diffusivity and conductivity, is considered when the closure of $A_i$ possesses a locally finite intersection property with any bounded domain of $\bbfR^d$ and all of $A_i$ have locally finite lower Minkowski content. A Markov process associated is then given in the form of Skorokhod decomposition with a local time, a bounded variation process concentrated on $\bigcup_i\partial A_i$. The process involving phase transition with finite number of phases and fusion temperatures is also obtained by using a limiting procedure. This process is a continuous martingale, which may reveal some information of the free boundary problem.
[Gong Guanglu (Beijing)]

MSC 2000:: *60J65 Brownian motion
60J60 Diffusion processes
60J35 Transition functions

Keywords: thermal conductivity; Minkowski content; Stefan problem

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]