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Equivalence of Pointwise and Global Ellipticity Estimates
Author(s) -
Vogt Hendrik
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200204)237:1<125::aid-mana125>3.0.co;2-3
Subject(s) - pointwise , mathematics , equivalence (formal languages) , pure mathematics , mathematical analysis , function (biology) , operator (biology) , order (exchange) , pointwise convergence , biochemistry , chemistry , approx , finance , repressor , evolutionary biology , gene , transcription factor , computer science , economics , biology , operating system
When defining an elliptic operator –∇ · ( a ∇) via the form method, one normally imposes pointwise conditions on the matrix valued function a in order to get positivity, ellipticity and sectoriality of the form. In this note we show that the pointwise conditions on a are equivalent to the corresponding global ones on the form.