This Article Full Text (PDF) All Versions of this Article: 1081286507081960v1 14/5/445    most recent References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via Scopus Google Scholar Articles by Silhavy, M. Social Bookmarking                         What's this?

The Divergence Theorem for Divergence Measure Vectorfields on Sets with Fractal Boundaries

M. ilhav

Institute of Mathematics of the AV R, itna 25, 115 67 Prague 1, Czech Republic

A divergence measure vectorfield is an ⁿ valued measure on an open subset U of ⁿ whose weak divergence in U is a (signed) measure. The paper uses the product rule for the product of the divergence measure by a function from W ^1, (U) 3 established in ilhav [ilhav, M., submitted, 2007] to prove the divergence theorem for the divergence measure vectorfields on bounded open sets U. It is shown that the surface integral of the normal component of the vectorfield occurring in the classical divergence theorem has to be replaced by a continuous linear functional on the space of Lipschitz functions on the boundary1 the volume integral contains the duality pairing occurring in the product rule. The boundary of U is arbitrary, it can be even fractal in the sense that the normal to U cannot be defined.

Key Words: Divergence measure vectorfields • normal trace

This version was published on July 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 5, 445-455 (2009)
DOI: 10.1177/1081286507081960


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?