A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight

<p>Abstract</p> <p>This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1029-242X-2011-58-i1"><m:mi mathvariant="script&quo...

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Main Authors:	Hongya Gao, Jinjing Qiao
Format:	Article
Language:	English
Published:	SpringerOpen 2011-01-01
Series:	Journal of Inequalities and Applications
Subjects:	Caccioppoli-type estimate very weak solution obstacle problem Mucken-houpt weight <inline-formula><m:math name="1029-242X-2011-58-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="script">A</m:mi> </m:math> </inline-formula>-harmonic equation
Online Access:	http://www.journalofinequalitiesandapplications.com/content/2011/1/58

id	doaj-cd591687da3d4931ad68437ffe99516b
record_format	Article
spelling	doaj-cd591687da3d4931ad68437ffe99516b2020-11-24T21:13:49ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011158A Caccioppoli-type estimate for very weak solutions to obstacle problems with weightHongya GaoJinjing Qiao<p>Abstract</p> <p>This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1029-242X-2011-58-i1"><m:mi mathvariant="script">A</m:mi></m:math> </inline-formula>-harmonic equation <inline-formula><m:math name="1029-242X-2011-58-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mstyle class="text"> <m:mtext class="textsf" mathvariant="sans-serif">div</m:mtext> </m:mstyle> <m:mi mathvariant="script">A</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mo class="MathClass-op">∇</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mn>0</m:mn> </m:math> </inline-formula> with <inline-formula><m:math name="1029-242X-2011-58-i3" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mo class="MathClass-rel">\|</m:mo> <m:mi mathvariant="script">A</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">\|</m:mo> <m:mo class="MathClass-rel">≈</m:mo> <m:mi>w</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">\|</m:mo> <m:mi>ξ</m:mi> <m:msup> <m:mrow> <m:mo class="MathClass-rel">\|</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> </inline-formula>, where 1 < <it>p </it>< ∞ and <it>w</it>(<it>x</it>) be a Muckenhoupt <it>A</it><sub>1 </sub>weight.</p> <p><b>Mathematics Subject Classification (2000) </b>35J50, 35J60</p> http://www.journalofinequalitiesandapplications.com/content/2011/1/58Caccioppoli-type estimatevery weak solutionobstacle problemMucken-houpt weight<inline-formula><m:math name="1029-242X-2011-58-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="script">A</m:mi> </m:math> </inline-formula>-harmonic equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hongya Gao Jinjing Qiao
spellingShingle	Hongya Gao Jinjing Qiao A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight Journal of Inequalities and Applications Caccioppoli-type estimate very weak solution obstacle problem Mucken-houpt weight <inline-formula><m:math name="1029-242X-2011-58-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="script">A</m:mi> </m:math> </inline-formula>-harmonic equation
author_facet	Hongya Gao Jinjing Qiao
author_sort	Hongya Gao
title	A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
title_short	A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
title_full	A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
title_fullStr	A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
title_full_unstemmed	A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight
title_sort	caccioppoli-type estimate for very weak solutions to obstacle problems with weight
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1025-5834 1029-242X
publishDate	2011-01-01
description	<p>Abstract</p> <p>This paper gives a Caccioppoli-type estimate for very weak solutions to obstacle problems of the <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1029-242X-2011-58-i1"><m:mi mathvariant="script">A</m:mi></m:math> </inline-formula>-harmonic equation <inline-formula><m:math name="1029-242X-2011-58-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mstyle class="text"> <m:mtext class="textsf" mathvariant="sans-serif">div</m:mtext> </m:mstyle> <m:mi mathvariant="script">A</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mo class="MathClass-op">∇</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">=</m:mo> <m:mn>0</m:mn> </m:math> </inline-formula> with <inline-formula><m:math name="1029-242X-2011-58-i3" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mo class="MathClass-rel">\|</m:mo> <m:mi mathvariant="script">A</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo class="MathClass-punc">,</m:mo> <m:mi>ξ</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">\|</m:mo> <m:mo class="MathClass-rel">≈</m:mo> <m:mi>w</m:mi> <m:mrow> <m:mo class="MathClass-open">(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo class="MathClass-close">)</m:mo> </m:mrow> <m:mo class="MathClass-rel">\|</m:mo> <m:mi>ξ</m:mi> <m:msup> <m:mrow> <m:mo class="MathClass-rel">\|</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mo class="MathClass-bin">-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> </m:math> </inline-formula>, where 1 < <it>p </it>< ∞ and <it>w</it>(<it>x</it>) be a Muckenhoupt <it>A</it><sub>1 </sub>weight.</p> <p><b>Mathematics Subject Classification (2000) </b>35J50, 35J60</p>
topic	Caccioppoli-type estimate very weak solution obstacle problem Mucken-houpt weight <inline-formula><m:math name="1029-242X-2011-58-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="script">A</m:mi> </m:math> </inline-formula>-harmonic equation
url	http://www.journalofinequalitiesandapplications.com/content/2011/1/58
work_keys_str_mv	AT hongyagao acaccioppolitypeestimateforveryweaksolutionstoobstacleproblemswithweight AT jinjingqiao acaccioppolitypeestimateforveryweaksolutionstoobstacleproblemswithweight AT hongyagao caccioppolitypeestimateforveryweaksolutionstoobstacleproblemswithweight AT jinjingqiao caccioppolitypeestimateforveryweaksolutionstoobstacleproblemswithweight
_version_	1716748008851243008

A Caccioppoli-type estimate for very weak solutions to obstacle problems with weight

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