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Weighted positivity of second order elliptic systems
Department of Mathematics, The Ohio State University, Columbus OH, USA.
Department of Mathematics, The Ohio State University, Columbus OH, USA.
2007 (English)In: Potential Analysis, ISSN 0926-2601, E-ISSN 1572-929X, Vol. 27, no 3, 251-270 p.Article in journal (Refereed) Published
Abstract [en]

Integral inequalities that concern the weighted positivity of a differential operator have important applications in qualitative theory of elliptic boundary value problems. Despite the power of these inequalities, however, it is far from clear which operators have this property. In this paper, we study weighted integral inequalities for general second order elliptic systems in ℝ n (n ≥ 3) and prove that, with a weight, smooth and positive homogeneous of order 2–n, the system is weighted positive only if the weight is the fundamental matrix of the system, possibly multiplied by a semi-positive definite constant matrix.

Place, publisher, year, edition, pages
Springer Netherlands, 2007. Vol. 27, no 3, 251-270 p.
Keyword [en]
Weighted positivity - Elliptic system - Fundamental matrix
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-40050DOI: 10.1007/s11118-007-9058-0ISI: 000248913600004Local ID: 52190OAI: oai:DiVA.org:liu-40050DiVA: diva2:260899
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13Bibliographically approved

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Maz´ya, Vladimir G.

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