Embedding operators of Sobolev spaces with variable exponents and applications
We introduce the vector-valued Sobolev spaces W m , p ( x ) (Ω; E 0 , E ) with variable exponent associated with two Banach spaces E 0 and E . The most regular space E α is found such that the differential operator D α is bounded and compact from W m , p ( x ) (Ω; E 0 , E ) to L q ( x ) (Ω; E α ), w...
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| Veröffentlicht in: | Analysis mathematica (Budapest) 2015-12, Vol.41 (4), p.273-297 |
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| container_title | Analysis mathematica (Budapest) |
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| creator | Shakhmurov, Veli B. |
| description | We introduce the vector-valued Sobolev spaces
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) with variable exponent associated with two Banach spaces
E
0
and
E
. The most regular space
E
α
is found such that the differential operator
D
α
is bounded and compact from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
L
q
(
x
)
(Ω;
E
α
), where
E
α
are interpolation spaces between
E
0
and
E
is depending on
α
= (
α
1
,
α
2
,...,
α
n
) and the positive integer
m
, where Ω ⊂ ℝ
n
is a region such that there exists a bounded linear extension operator from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
W
m
,
p
(
x
)
(ℝ
n
;
E
(
A
),
E
). The function
p
(
x
) is Lipschitz continuous on Ω and
q
(
x
) is a measurable function such that
for a.e.
. Ehrling–Nirenberg–Gagilardo type sharp estimates for mixed derivatives are obtained. Then, by using this embedding result, the separability properties of abstract differential equations are established. |
| doi_str_mv | 10.1007/s10476-015-0303-2 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1808111212</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1808111212</sourcerecordid><originalsourceid>FETCH-LOGICAL-c321t-80c13d64500d02cae347e34a3ccc45377ac96e6327b850e1a7be13aec310e1a3</originalsourceid><addsrcrecordid>eNp9kD1PwzAQhi0EEqXwA9g8sgTu7CR2R1SVD6mCgQ5sluNcS6rUDnZa4N-TKswMp1cnPe9J9zB2jXCLAOouIeSqzACLDCTITJywCRZaZ0LJ91M2AZQyk7oQ5-wipS0AzEotJ-xlsauorhu_4aGjaPsQEw9r_haq0NKBp846Svyr6T_4wcbGVi1x-u6CJ98nbn3Nbde1jbN9E3y6ZGdr2ya6-sspWz0sVvOnbPn6-Dy_X2ZOCuwzDQ5lXeYFQA3CWZK5GsZK51xeSKWsm5VUSqEqXQChVRWhtOQkHjc5ZTfj2S6Gzz2l3uya5KhtraewTwY1aEQUKAYUR9TFkFKktelis7PxxyCYozozqjODOnNUZ44dMXbSwPoNRbMN--iHh_4p_QJ4-nG_</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1808111212</pqid></control><display><type>article</type><title>Embedding operators of Sobolev spaces with variable exponents and applications</title><source>SpringerLink Journals - AutoHoldings</source><creator>Shakhmurov, Veli B.</creator><creatorcontrib>Shakhmurov, Veli B.</creatorcontrib><description>We introduce the vector-valued Sobolev spaces
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) with variable exponent associated with two Banach spaces
E
0
and
E
. The most regular space
E
α
is found such that the differential operator
D
α
is bounded and compact from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
L
q
(
x
)
(Ω;
E
α
), where
E
α
are interpolation spaces between
E
0
and
E
is depending on
α
= (
α
1
,
α
2
,...,
α
n
) and the positive integer
m
, where Ω ⊂ ℝ
n
is a region such that there exists a bounded linear extension operator from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
W
m
,
p
(
x
)
(ℝ
n
;
E
(
A
),
E
). The function
p
(
x
) is Lipschitz continuous on Ω and
q
(
x
) is a measurable function such that
for a.e.
. Ehrling–Nirenberg–Gagilardo type sharp estimates for mixed derivatives are obtained. Then, by using this embedding result, the separability properties of abstract differential equations are established.</description><identifier>ISSN: 0133-3852</identifier><identifier>EISSN: 1588-273X</identifier><identifier>DOI: 10.1007/s10476-015-0303-2</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Analysis ; Banach space ; Derivatives ; Estimates ; Exponents ; Integers ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Operators ; Sobolev space</subject><ispartof>Analysis mathematica (Budapest), 2015-12, Vol.41 (4), p.273-297</ispartof><rights>Akadémiai Kiadó, Budapest, Hungary 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-80c13d64500d02cae347e34a3ccc45377ac96e6327b850e1a7be13aec310e1a3</citedby><cites>FETCH-LOGICAL-c321t-80c13d64500d02cae347e34a3ccc45377ac96e6327b850e1a7be13aec310e1a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10476-015-0303-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10476-015-0303-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Shakhmurov, Veli B.</creatorcontrib><title>Embedding operators of Sobolev spaces with variable exponents and applications</title><title>Analysis mathematica (Budapest)</title><addtitle>Anal Math</addtitle><description>We introduce the vector-valued Sobolev spaces
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) with variable exponent associated with two Banach spaces
E
0
and
E
. The most regular space
E
α
is found such that the differential operator
D
α
is bounded and compact from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
L
q
(
x
)
(Ω;
E
α
), where
E
α
are interpolation spaces between
E
0
and
E
is depending on
α
= (
α
1
,
α
2
,...,
α
n
) and the positive integer
m
, where Ω ⊂ ℝ
n
is a region such that there exists a bounded linear extension operator from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
W
m
,
p
(
x
)
(ℝ
n
;
E
(
A
),
E
). The function
p
(
x
) is Lipschitz continuous on Ω and
q
(
x
) is a measurable function such that
for a.e.
. Ehrling–Nirenberg–Gagilardo type sharp estimates for mixed derivatives are obtained. Then, by using this embedding result, the separability properties of abstract differential equations are established.</description><subject>Analysis</subject><subject>Banach space</subject><subject>Derivatives</subject><subject>Estimates</subject><subject>Exponents</subject><subject>Integers</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators</subject><subject>Sobolev space</subject><issn>0133-3852</issn><issn>1588-273X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwA9g8sgTu7CR2R1SVD6mCgQ5sluNcS6rUDnZa4N-TKswMp1cnPe9J9zB2jXCLAOouIeSqzACLDCTITJywCRZaZ0LJ91M2AZQyk7oQ5-wipS0AzEotJ-xlsauorhu_4aGjaPsQEw9r_haq0NKBp846Svyr6T_4wcbGVi1x-u6CJ98nbn3Nbde1jbN9E3y6ZGdr2ya6-sspWz0sVvOnbPn6-Dy_X2ZOCuwzDQ5lXeYFQA3CWZK5GsZK51xeSKWsm5VUSqEqXQChVRWhtOQkHjc5ZTfj2S6Gzz2l3uya5KhtraewTwY1aEQUKAYUR9TFkFKktelis7PxxyCYozozqjODOnNUZ44dMXbSwPoNRbMN--iHh_4p_QJ4-nG_</recordid><startdate>20151201</startdate><enddate>20151201</enddate><creator>Shakhmurov, Veli B.</creator><general>Springer Netherlands</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20151201</creationdate><title>Embedding operators of Sobolev spaces with variable exponents and applications</title><author>Shakhmurov, Veli B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-80c13d64500d02cae347e34a3ccc45377ac96e6327b850e1a7be13aec310e1a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis</topic><topic>Banach space</topic><topic>Derivatives</topic><topic>Estimates</topic><topic>Exponents</topic><topic>Integers</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators</topic><topic>Sobolev space</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shakhmurov, Veli B.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Analysis mathematica (Budapest)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shakhmurov, Veli B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Embedding operators of Sobolev spaces with variable exponents and applications</atitle><jtitle>Analysis mathematica (Budapest)</jtitle><stitle>Anal Math</stitle><date>2015-12-01</date><risdate>2015</risdate><volume>41</volume><issue>4</issue><spage>273</spage><epage>297</epage><pages>273-297</pages><issn>0133-3852</issn><eissn>1588-273X</eissn><abstract>We introduce the vector-valued Sobolev spaces
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) with variable exponent associated with two Banach spaces
E
0
and
E
. The most regular space
E
α
is found such that the differential operator
D
α
is bounded and compact from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
L
q
(
x
)
(Ω;
E
α
), where
E
α
are interpolation spaces between
E
0
and
E
is depending on
α
= (
α
1
,
α
2
,...,
α
n
) and the positive integer
m
, where Ω ⊂ ℝ
n
is a region such that there exists a bounded linear extension operator from
W
m
,
p
(
x
)
(Ω;
E
0
,
E
) to
W
m
,
p
(
x
)
(ℝ
n
;
E
(
A
),
E
). The function
p
(
x
) is Lipschitz continuous on Ω and
q
(
x
) is a measurable function such that
for a.e.
. Ehrling–Nirenberg–Gagilardo type sharp estimates for mixed derivatives are obtained. Then, by using this embedding result, the separability properties of abstract differential equations are established.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10476-015-0303-2</doi><tpages>25</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0133-3852 |
| ispartof | Analysis mathematica (Budapest), 2015-12, Vol.41 (4), p.273-297 |
| issn | 0133-3852 1588-273X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1808111212 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Analysis Banach space Derivatives Estimates Exponents Integers Mathematical analysis Mathematics Mathematics and Statistics Operators Sobolev space |
| title | Embedding operators of Sobolev spaces with variable exponents and applications |
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