Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type
We study general parabolic equations of the form u t = div A ( x , t , u , D u ) + div ( | F | p - 2 F ) + f whose principal part depends on the solution itself. The vector field A is assumed to have small mean oscillation in x , measurable in t , Lipschitz continuous in u , and its growth in Du is...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2017-12, Vol.56 (6), p.1-42, Article 173 |
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| container_title | Calculus of variations and partial differential equations |
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| creator | Nguyen, Truyen |
| description | We study general parabolic equations of the form
u
t
=
div
A
(
x
,
t
,
u
,
D
u
)
+
div
(
|
F
|
p
-
2
F
)
+
f
whose principal part depends on the solution itself. The vector field
A
is assumed to have small mean oscillation in
x
, measurable in
t
, Lipschitz continuous in
u
, and its growth in
Du
is like the
p
-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when
p
>
2
n
/
(
n
+
2
)
. This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York,
1993
) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320,
2007
). |
| doi_str_mv | 10.1007/s00526-017-1265-y |
| format | Article |
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u
t
=
div
A
(
x
,
t
,
u
,
D
u
)
+
div
(
|
F
|
p
-
2
F
)
+
f
whose principal part depends on the solution itself. The vector field
A
is assumed to have small mean oscillation in
x
, measurable in
t
, Lipschitz continuous in
u
, and its growth in
Du
is like the
p
-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when
p
>
2
n
/
(
n
+
2
)
. This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York,
1993
) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320,
2007
).</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-017-1265-y</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Calculus of Variations and Optimal Control; Optimization ; Control ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Perturbation methods ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2017-12, Vol.56 (6), p.1-42, Article 173</ispartof><rights>Springer-Verlag GmbH Germany 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-c8b538c6584d300061d825aa980202eea215fde140b599771a5598d696b28763</citedby><cites>FETCH-LOGICAL-c316t-c8b538c6584d300061d825aa980202eea215fde140b599771a5598d696b28763</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/s00526-017-1265-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-017-1265-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Nguyen, Truyen</creatorcontrib><title>Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We study general parabolic equations of the form
u
t
=
div
A
(
x
,
t
,
u
,
D
u
)
+
div
(
|
F
|
p
-
2
F
)
+
f
whose principal part depends on the solution itself. The vector field
A
is assumed to have small mean oscillation in
x
, measurable in
t
, Lipschitz continuous in
u
, and its growth in
Du
is like the
p
-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when
p
>
2
n
/
(
n
+
2
)
. This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York,
1993
) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320,
2007
).</description><subject>Analysis</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Perturbation methods</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kD1OwzAUxy0EEqVwADZLzIZnO3acEVV8VKrE0onFchKnSpXaqZ0M2bgDR-EI3ISTYBQkJqY3vN__ffwQuqZwSwHyuwggmCRAc0KZFGQ6QQuacUZAcXGKFlBkGWFSFufoIsY9ABWKZQu0W7vBhtYHvDJdbcPnh_t6e3-ddofR1djGoT2YwUbcJCL6bhxa7yIePN5ZZ4PpcG-CKX3XVtgeRzO3fYN7sjF9Z6rWODxMvb1EZ43por36rUu0fXzYrp7J5uVpvbrfkIpTOZBKlYKrSgqV1RwAJK0VE8YUChgwaw2joqktzaAURZHn1AhRqFoWsmQql3yJbuaxffDHMZ2v934MLm3UDCQXgjNOE0Vnqgo-xmAb3Yf0Z5g0Bf2jU886ddKpf3TqKWXYnImJdTsb_ib_H_oGdk96bw</recordid><startdate>20171201</startdate><enddate>20171201</enddate><creator>Nguyen, Truyen</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20171201</creationdate><title>Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type</title><author>Nguyen, Truyen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-c8b538c6584d300061d825aa980202eea215fde140b599771a5598d696b28763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Perturbation methods</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nguyen, Truyen</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nguyen, Truyen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2017-12-01</date><risdate>2017</risdate><volume>56</volume><issue>6</issue><spage>1</spage><epage>42</epage><pages>1-42</pages><artnum>173</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We study general parabolic equations of the form
u
t
=
div
A
(
x
,
t
,
u
,
D
u
)
+
div
(
|
F
|
p
-
2
F
)
+
f
whose principal part depends on the solution itself. The vector field
A
is assumed to have small mean oscillation in
x
, measurable in
t
, Lipschitz continuous in
u
, and its growth in
Du
is like the
p
-Laplace operator. We establish interior Calderón–Zygmund estimates for locally bounded weak solutions to the equations when
p
>
2
n
/
(
n
+
2
)
. This is achieved by employing a perturbation method together with developing a two-parameter technique and a new compactness argument. We also make crucial use of the intrinsic geometry method by DiBenedetto (Degenerate parabolic equations, Springer, New York,
1993
) and the maximal function free approach by Acerbi and Mingione (Duke Math J 136(2):285–320,
2007
).</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-017-1265-y</doi><tpages>42</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0944-2669 |
| ispartof | Calculus of variations and partial differential equations, 2017-12, Vol.56 (6), p.1-42, Article 173 |
| issn | 0944-2669 1432-0835 |
| language | eng |
| recordid | cdi_proquest_journals_2063553231 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Calculus of Variations and Optimal Control Optimization Control Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Operators (mathematics) Perturbation methods Systems Theory Theoretical |
| title | Interior Calderón–Zygmund estimates for solutions to general parabolic equations of p-Laplacian type |
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