Search results for "26D10"

showing 2 items of 2 documents

Poincaré inequalities and Steiner symmetrization

1996

A complete geometric characterization for a general Steiner symmetric domain Ω ⊂ Rn to satisfy the Poincare inequality with exponent p > n−1 is obtained and it is shown that this range of exponents is best possible. In the case where the Steiner symmetric domain is determined by revolving the graph of a Lipschitz continuous function, it is shown that the preceding characterization works for all p > 1 and furthermore for such domains a geometric characterization for a more general Sobolev–Poincare inequality to hold is given. Although the operation of Steiner symmetrization need not always preserve a Poincare inequality, a general class of domains is given for which Poincare inequalities are…

Finite volume methodGeneral MathematicsA domainPoincaré inequalityLipschitz continuityCombinatoricssymbols.namesakeinequalitiesPoincaré conjecturesymbolsExponentSymmetrization46E35Locally integrable function26D10Mathematics
researchProduct

Korn inequality on irregular domains

2013

Abstract In this paper, we study the weighted Korn inequality on some irregular domains, e.g., s-John domains and domains satisfying quasihyperbolic boundary conditions. Examples regarding sharpness of the Korn inequality on these domains are presented. Moreover, we show that Korn inequalities imply certain Poincare inequality.

Pure mathematicsInequalityKorn inequalityquasihyperbolic metricApplied Mathematicsmedia_common.quotation_subjectta111Mathematics::Analysis of PDEss-John domainPoincaré inequalitysymbols.namesakeMathematics - Analysis of PDEsMathematics - Classical Analysis and ODEsPoincaré inequalityClassical Analysis and ODEs (math.CA)FOS: Mathematicssymbolsdivergence equationBoundary value problem26D10 35A23AnalysisAnalysis of PDEs (math.AP)Mathematicsmedia_commonJournal of Mathematical Analysis and Applications
researchProduct