2005-11-17Buch DOI: 10.18452/2711
A Generalization of the Fundamental Estimates for Wm,p- Solutions of Linear Systems with Constant Coefficients (the case 1 < p < 2)
 dc.contributor.author Wolf, Jörg dc.date.accessioned 2017-06-15T18:03:17Z dc.date.available 2017-06-15T18:03:17Z dc.date.created 2005-11-17 dc.date.issued 2005-11-17 dc.identifier.issn 0863-0976 dc.identifier.uri http://edoc.hu-berlin.de/18452/3363 dc.description.abstract The aim of the present paper is to extent the well known fundamental estimates (w.r.t. the $L^2$-norm) for weak solutions of a linear elliptic system with constant coefficients: $\sum_{ j= 1}^ N \sum_{\mid \alpha\mid,\mid \beta\mid = m} D^\alpha (A_{ij}^{\alpha\beta} D^\beta u^j)=0 \quad \mbox{in}\;\; \Omega\quad(i=1,\ldots,N),$ where $\nu_\circ\!\parallel\!\! \xi\!\!\parallel^2 \leq A_{ij}^{\alpha\beta}\xi_\alpha^i \xi_\beta^j \leq c_\circ \parallel\!\! \xi\!\!\parallel^2\;\forall\xi\in \R^{nN}, (\Omega\subset \R^n$ is open and bounded). Based on a generalization of the "CACCOIOPPOLI - inequality" we are able to establish the extended fundamental estimates w.r.t. the $L^p$- norm of $W^m,p$- solutions (1 < p < 2) of the linear system. eng dc.language.iso eng dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject elliptic systems eng dc.subject multiplicative inequality eng dc.subject fundamental estimate eng dc.subject.ddc 510 Mathematik dc.title A Generalization of the Fundamental Estimates for Wm,p- Solutions of Linear Systems with Constant Coefficients (the case 1 < p < 2) dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10053852 dc.identifier.doi http://dx.doi.org/10.18452/2711 local.edoc.container-title Preprints aus dem Institut für Mathematik local.edoc.pages 13 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 1997 local.edoc.container-issue 11 local.edoc.container-year 1997 local.edoc.container-erstkatid 2075199-0