FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2074702479> ?p ?o ?g. }

• W2074702479 endingPage "1188" @default.
• W2074702479 startingPage "1179" @default.
• W2074702479 abstract "A domain <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D subset-of double-struck upper R Superscript n> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>D subset {mathbb {R}^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has the quasiconformal extension property if each quasiconformal self-map of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=application/x-tex>D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> extends to a quasiconformal self-map of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R Superscript n Baseline semicolon upper D> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:mo>;</mml:mo> <mml:mspace width=thickmathspace /> <mml:mi>D</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb {R}^n};;D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has the Sobolev extension property if there is a bounded linear operator <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Lamda colon upper W Superscript 1 comma n Baseline left-parenthesis upper D right-parenthesis right-arrow upper W Superscript 1 comma n Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi mathvariant=normal>Λ<!-- Λ --></mml:mi> <mml:mo>:</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>W</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Lambda :{W^{1,n}}(D) to {W^{1,n}}({mathbb {R}^n})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We consider the relation between the above extension properties for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-slanted-equals 3> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>⩾<!-- ⩾ --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n geqslant 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that for domains quasiconformally equivalent to a ball the quasiconformal extension property implies the Sobolev extension property. We show that this is not true in general. Next the Sobolev extension property does not imply the extension property for quasiconformal maps which extend as homeomorphisms. Finally if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G subset-of double-struck upper R squared> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>G subset {mathbb {R}^2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D equals upper G times double-struck upper R> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mi>G</mml:mi> <mml:mo>×<!-- × --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>D = G times mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is quasiconformally equivalent to a ball, then <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=application/x-tex>D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has the quasiconformal extension property if and only if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding=application/x-tex>D</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a quasiball." @default.
• W2074702479 created "2016-06-24" @default.
• W2074702479 creator A5032969852 @default.
• W2074702479 date "1993-01-01" @default.
• W2074702479 modified "2023-09-26" @default.
• W2074702479 title "Sobolev and quasiconformal extension domains" @default.
• W2074702479 cites W1553738528 @default.
• W2074702479 cites W1972185031 @default.
• W2074702479 cites W1996267863 @default.
• W2074702479 cites W2009955818 @default.
• W2074702479 cites W2032925799 @default.
• W2074702479 cites W2036154812 @default.
• W2074702479 cites W2044605258 @default.
• W2074702479 cites W2071210518 @default.
• W2074702479 cites W2074145476 @default.
• W2074702479 cites W2088262139 @default.
• W2074702479 cites W2126881652 @default.
• W2074702479 cites W2327359167 @default.
• W2074702479 cites W26105898 @default.
• W2074702479 cites W4238932019 @default.
• W2074702479 doi "https://doi.org/10.1090/s0002-9939-1993-1169028-7" @default.
• W2074702479 hasPublicationYear "1993" @default.
• W2074702479 type Work @default.
• W2074702479 sameAs 2074702479 @default.
• W2074702479 citedByCount "2" @default.
• W2074702479 countsByYear W20747024792018 @default.
• W2074702479 crossrefType "journal-article" @default.
• W2074702479 hasAuthorship W2074702479A5032969852 @default.
• W2074702479 hasBestOaLocation W20747024791 @default.
• W2074702479 hasConcept C11413529 @default.
• W2074702479 hasConcept C154945302 @default.
• W2074702479 hasConcept C2776321320 @default.
• W2074702479 hasConcept C41008148 @default.
• W2074702479 hasConceptScore W2074702479C11413529 @default.
• W2074702479 hasConceptScore W2074702479C154945302 @default.
• W2074702479 hasConceptScore W2074702479C2776321320 @default.
• W2074702479 hasConceptScore W2074702479C41008148 @default.
• W2074702479 hasIssue "4" @default.
• W2074702479 hasLocation W20747024791 @default.
• W2074702479 hasOpenAccess W2074702479 @default.
• W2074702479 hasPrimaryLocation W20747024791 @default.
• W2074702479 hasRelatedWork W151193258 @default.
• W2074702479 hasRelatedWork W1529400504 @default.
• W2074702479 hasRelatedWork W1871911958 @default.
• W2074702479 hasRelatedWork W1892467659 @default.
• W2074702479 hasRelatedWork W2348710178 @default.
• W2074702479 hasRelatedWork W2808586768 @default.
• W2074702479 hasRelatedWork W2998403542 @default.
• W2074702479 hasRelatedWork W3016716103 @default.
• W2074702479 hasRelatedWork W3107474891 @default.
• W2074702479 hasRelatedWork W38394648 @default.
• W2074702479 hasVolume "119" @default.
• W2074702479 isParatext "false" @default.
• W2074702479 isRetracted "false" @default.
• W2074702479 magId "2074702479" @default.
• W2074702479 workType "article" @default.