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Weighted Poincaré and Korn inequalities for Hölder α domains
Author(s) -
Acosta Gabriel,
Durán Ricardo G.,
Lombardi Ariel L.
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.680
Subject(s) - mathematics , inequality , poincaré conjecture , argument (complex analysis) , boundary (topology) , pure mathematics , poincaré inequality , type (biology) , mathematical economics , mathematical analysis , ecology , biochemistry , chemistry , biology
Abstract It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper, we prove a family of weaker inequalities for this kind of domains, replacing the standard L p ‐norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kondratiev and Oleinik, we show that weighted Korn inequalities can be derived from them. The Poincaré type inequalities proved here improve previously known results. We show by means of examples that our results are optimal. Copyright © 2005 John Wiley & Sons, Ltd.