English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We give a Dirichlet form approach for the construction of a distortedBrownian motion in $E := [0;\infty)^n$, $n\in\mathbb{N}$, where the behavior onthe boundary is determined by the competing effects of reflection from andpinning at the boundary. The problem is formulated in an $L^2$-setting withunderlying measure $\mu=\varrho m$. Here $\varrho$ is a positive density,integrable with respect to the measure $m$ and fulfilling the Hamza condition.The measure $m$ is such that the boundary of $E$ is not of $m$-measure zero. Areference measure of this type is needed in order to give meaning to theso-called Wentzell boundary condition which is in literature typical formodeling such kind of boundary behavior. In providing a Skorokhod decompositionof the constructed process we are able to justify that the stochastic processis solving the underlying stochastic differential equation weakly in the senseof N. Ikeda and Sh. Watanabe for quasi every starting point. At the boundarythe constructed process indeed is governed by the competing effects ofreflection and pinning. In order to obtain the Skorokhod decomposition we need$\varrho$ to be continuously differentiable on $E$, which is equivalent tocontinuity of the logarithmic derivative of $\varrho$. Furthermore, we assumethat the logarithmic derivative of $\varrho$ is square integrable with respectto $\mu$. We do not need that the logarithmic derivative of $\varrho$ isLipschitz continuous. In particular, our considerations enable us to constructa dynamical wetting model (also known as Ginzburg-Landau dynamics) on a boundedset $D_N\subset\mathbb{Z}^d$ under mild assumptions on the underlying pairinteraction potentials in all dimensions $d\in\mathbb{N}$. In dimension $d=2$this model describes the motion of an interface resulting from wetting of asolid surface by a fluid.

Construction of a finite volume dynamical wetting model with \delta-pinning in (d+1)-dimension via Dirichlet forms