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...
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2007-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2007/034138 |
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doaj-6c3559260bfc4cbf8248952d8f314a0f2020-11-24T21:19:08ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2007-01-0120071034138On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous StructurePersson L-EChechkin GAKoroleva Yu O<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>http://www.journalofinequalitiesandapplications.com/content/2007/034138 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Persson L-E Chechkin GA Koroleva Yu O |
| spellingShingle |
Persson L-E Chechkin GA Koroleva Yu O On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure Journal of Inequalities and Applications |
| author_facet |
Persson L-E Chechkin GA Koroleva Yu O |
| author_sort |
Persson L-E |
| title |
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure |
| title_short |
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure |
| title_full |
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure |
| title_fullStr |
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure |
| title_full_unstemmed |
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure |
| title_sort |
on the precise asymptotics of the constant in friedrich's inequality for functions vanishing on the part of the boundary with microinhomogeneous structure |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2007-01-01 |
| description |
<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> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2007/034138 |
| work_keys_str_mv |
AT perssonle onthepreciseasymptoticsoftheconstantinfriedrichsinequalityforfunctionsvanishingonthepartoftheboundarywithmicroinhomogeneousstructure AT chechkinga onthepreciseasymptoticsoftheconstantinfriedrichsinequalityforfunctionsvanishingonthepartoftheboundarywithmicroinhomogeneousstructure AT korolevayuo onthepreciseasymptoticsoftheconstantinfriedrichsinequalityforfunctionsvanishingonthepartoftheboundarywithmicroinhomogeneousstructure |
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1726006829014581248 |