Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces
In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted L q -maximal regularity in weighted Bes...
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| Veröffentlicht in: | Potential analysis 2022-12, Vol.57 (4), p.601-669 |
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| creator | Hummel, Felix Lindemulder, Nick |
| description | In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted
L
q
-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt
A
∞
-class. In the Besov space case we have the restriction that the microscopic parameter equals to
q
. Going beyond the
A
p
-range, where
p
is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators. |
| doi_str_mv | 10.1007/s11118-021-09929-w |
| format | Article |
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L
q
-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt
A
∞
-class. In the Besov space case we have the restriction that the microscopic parameter equals to
q
. Going beyond the
A
p
-range, where
p
is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators.</description><identifier>ISSN: 0926-2601</identifier><identifier>EISSN: 1572-929X</identifier><identifier>DOI: 10.1007/s11118-021-09929-w</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Boundary conditions ; Boundary value problems ; Flexibility ; Function space ; Functional Analysis ; Geometry ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Parameters ; Potential Theory ; Probability Theory and Stochastic Processes ; Regularity</subject><ispartof>Potential analysis, 2022-12, Vol.57 (4), p.601-669</ispartof><rights>The Author(s) 2021</rights><rights>The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-f12ee678066928df4d705db496d8c6107204d7421d2362efc4935bf5149f9b5d3</citedby><cites>FETCH-LOGICAL-c363t-f12ee678066928df4d705db496d8c6107204d7421d2362efc4935bf5149f9b5d3</cites><orcidid>0000-0002-2374-7030</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11118-021-09929-w$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11118-021-09929-w$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Hummel, Felix</creatorcontrib><creatorcontrib>Lindemulder, Nick</creatorcontrib><title>Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces</title><title>Potential analysis</title><addtitle>Potential Anal</addtitle><description>In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted
L
q
-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt
A
∞
-class. In the Besov space case we have the restriction that the microscopic parameter equals to
q
. Going beyond the
A
p
-range, where
p
is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators.</description><subject>Boundary conditions</subject><subject>Boundary value problems</subject><subject>Flexibility</subject><subject>Function space</subject><subject>Functional Analysis</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Parameters</subject><subject>Potential Theory</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Regularity</subject><issn>0926-2601</issn><issn>1572-929X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kE9LxDAQxYMouK5-AU8Bz9FJ0iTNUZfdVVlwwb-30Dbp2qXb1qRl8dsbreDNuQwzvPeG-SF0TuGSAqirQGOlBBgloDXTZH-AJlQoRuLwdogmoJkkTAI9RichbAGAKZVO0P28rquurwqcNRavM5_lbR2nm3ZobOY_8UtWDw6vfZvXbhdw1eBXV23ee2fxYmiKvmob_NhlhQun6KjM6uDOfvsUPS_mT7NbsnpY3s2uV6TgkvekpMw5qVKQUrPUlolVIGyeaGnTQlJQDOIqYdQyLpkri0RzkZeCJrrUubB8ii7G3M63H4MLvdm2g2_iScMUV4oLkaqoYqOq8G0I3pWm89UufmQomG9mZmRmIjPzw8zso4mPphDFzcb5v-h_XF-Sj26Q</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Hummel, Felix</creator><creator>Lindemulder, Nick</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2374-7030</orcidid></search><sort><creationdate>20221201</creationdate><title>Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces</title><author>Hummel, Felix ; Lindemulder, Nick</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-f12ee678066928df4d705db496d8c6107204d7421d2362efc4935bf5149f9b5d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Boundary conditions</topic><topic>Boundary value problems</topic><topic>Flexibility</topic><topic>Function space</topic><topic>Functional Analysis</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Parameters</topic><topic>Potential Theory</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Regularity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hummel, Felix</creatorcontrib><creatorcontrib>Lindemulder, Nick</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Potential analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hummel, Felix</au><au>Lindemulder, Nick</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces</atitle><jtitle>Potential analysis</jtitle><stitle>Potential Anal</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>57</volume><issue>4</issue><spage>601</spage><epage>669</epage><pages>601-669</pages><issn>0926-2601</issn><eissn>1572-929X</eissn><abstract>In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted
L
q
-maximal regularity in weighted Besov and Triebel-Lizorkin spaces for the parabolic case, where the spatial weight is a power weight in the Muckenhoupt
A
∞
-class. In the Besov space case we have the restriction that the microscopic parameter equals to
q
. Going beyond the
A
p
-range, where
p
is the integrability parameter of the Besov or Triebel-Lizorkin space under consideration, yields extra flexibility in the sharp regularity of the boundary inhomogeneities. This extra flexibility allows us to treat rougher boundary data and provides a quantitative smoothing effect on the interior of the domain. The main ingredient is an analysis of anisotropic Poisson operators.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s11118-021-09929-w</doi><tpages>69</tpages><orcidid>https://orcid.org/0000-0002-2374-7030</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Boundary conditions Boundary value problems Flexibility Function space Functional Analysis Geometry Mathematics Mathematics and Statistics Operators (mathematics) Parameters Potential Theory Probability Theory and Stochastic Processes Regularity |
| title | Elliptic and Parabolic Boundary Value Problems in Weighted Function Spaces |
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