On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure
<p/> <p>We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary <inline-formula><graphic file="1029-242X-2007-034138-i1.gif"/></inline-formula>. It is assumed that <in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2007/034138 |
| Summary: | <p/> <p>We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary <inline-formula><graphic file="1029-242X-2007-034138-i1.gif"/></inline-formula>. It is assumed that <inline-formula><graphic file="1029-242X-2007-034138-i2.gif"/></inline-formula> consists of <inline-formula><graphic file="1029-242X-2007-034138-i3.gif"/></inline-formula> pieces with diameter of order <inline-formula><graphic file="1029-242X-2007-034138-i4.gif"/></inline-formula>. In addition, <inline-formula><graphic file="1029-242X-2007-034138-i5.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2007-034138-i6.gif"/></inline-formula> as <inline-formula><graphic file="1029-242X-2007-034138-i7.gif"/></inline-formula>.</p> |
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| ISSN: | 1025-5834 1029-242X |