FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4214899414> ?p ?o ?g. }

• W4214899414 endingPage "779" @default.
• W4214899414 startingPage "749" @default.
• W4214899414 abstract "Abstract We study the Sobolev spaces <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>H</m:mi> <m:mi>σ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H^{sigma}(K)} and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msubsup> <m:mi>H</m:mi> <m:mn>0</m:mn> <m:mi>σ</m:mi> </m:msubsup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H^{sigma}_{0}(K)} on p.c.f. self-similar sets. First, for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>σ</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mo>+</m:mo> </m:msup> </m:mrow> </m:math> {sigmainmathbb{R}^{+}} , we make an exact description of the tangents of functions in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>H</m:mi> <m:mi>σ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H^{sigma}(K)} at the boundary, and introduce a countable set of critical orders that arises naturally in the boundary behavior of functions. These critical orders are just <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mfrac> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:mfrac> <m:mo>+</m:mo> <m:msub> <m:mi>ℤ</m:mi> <m:mo>+</m:mo> </m:msub> </m:mrow> </m:math> {frac{1}{2}+mathbb{Z}_{+}} in the Euclidean case, but become complicated on fractals. Second, we characterize <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msubsup> <m:mi>H</m:mi> <m:mn>0</m:mn> <m:mi>σ</m:mi> </m:msubsup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H_{0}^{sigma}(K)} as the space of functions in <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>H</m:mi> <m:mi>σ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H^{sigma}(K)} with tangents of appropriate order, that depend on σ and critical orders, being 0. Last, we extend <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msup> <m:mi>H</m:mi> <m:mi>σ</m:mi> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:math> {H^{sigma}(K)} to <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>σ</m:mi> <m:mo>∈</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:math> {sigmainmathbb{R}} , and obtain various interpolation theorems with <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>σ</m:mi> <m:mo>∈</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mo>+</m:mo> </m:msup> </m:mrow> </m:math> {sigmainmathbb{R}^{+}} or <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>σ</m:mi> <m:mo>∈</m:mo> <m:mi>ℝ</m:mi> </m:mrow> </m:math> {sigmainmathbb{R}} . The interpolation space presents a critical phenomenon when the resulted order <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mi>σ</m:mi> <m:mi>θ</m:mi> </m:msub> </m:math> {sigma_{theta}} is critical. Moreover, for the interpolation couple <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mrow> <m:msubsup> <m:mi>H</m:mi> <m:mn>0</m:mn> <m:mi>σ</m:mi> </m:msubsup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mrow> <m:msubsup> <m:mi>H</m:mi> <m:mn>0</m:mn> <m:msup> <m:mi>σ</m:mi> <m:mo>′</m:mo> </m:msup> </m:msubsup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:mi>K</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:math> {(H^{sigma}_{0}(K),H^{sigma^{prime}}_{0}(K))} , more than the classical theorem, our interpolation theorem fully covers the teratological case that <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mo stretchy=false>{</m:mo> <m:mi>σ</m:mi> <m:mo>,</m:mo> <m:msup> <m:mi>σ</m:mi> <m:mo>′</m:mo> </m:msup> <m:mo stretchy=false>}</m:mo> </m:mrow> </m:math> {{sigma,sigma^{prime}}} contains at least one critical order." @default.
• W4214899414 created "2022-03-05" @default.
• W4214899414 creator A5001620324 @default.
• W4214899414 creator A5083867120 @default.
• W4214899414 date "2022-03-01" @default.
• W4214899414 modified "2023-09-25" @default.
• W4214899414 title "Sobolev spaces on p.c.f. self-similar sets II: Boundary behavior and interpolation theorems" @default.
• W4214899414 cites W1667858656 @default.
• W4214899414 cites W187070328 @default.
• W4214899414 cites W1990522554 @default.
• W4214899414 cites W1991584117 @default.
• W4214899414 cites W2006368537 @default.
• W4214899414 cites W2010942491 @default.
• W4214899414 cites W2015968538 @default.
• W4214899414 cites W2024867873 @default.
• W4214899414 cites W2027990787 @default.
• W4214899414 cites W2028356180 @default.
• W4214899414 cites W2032786723 @default.
• W4214899414 cites W2047079374 @default.
• W4214899414 cites W2052225443 @default.
• W4214899414 cites W2063698374 @default.
• W4214899414 cites W2069391211 @default.
• W4214899414 cites W2074225920 @default.
• W4214899414 cites W2076682546 @default.
• W4214899414 cites W2085178161 @default.
• W4214899414 cites W2103051749 @default.
• W4214899414 cites W2113328955 @default.
• W4214899414 cites W2120340042 @default.
• W4214899414 cites W2132431236 @default.
• W4214899414 cites W2142149225 @default.
• W4214899414 cites W2151792428 @default.
• W4214899414 cites W2330973331 @default.
• W4214899414 cites W2620128442 @default.
• W4214899414 cites W2914417064 @default.
• W4214899414 cites W2963203761 @default.
• W4214899414 cites W3000265654 @default.
• W4214899414 cites W3093248291 @default.
• W4214899414 cites W3099863777 @default.
• W4214899414 cites W3102738815 @default.
• W4214899414 cites W3217314725 @default.
• W4214899414 cites W4235570091 @default.
• W4214899414 cites W4252915883 @default.
• W4214899414 cites W4302819252 @default.
• W4214899414 doi "https://doi.org/10.1515/forum-2021-0174" @default.
• W4214899414 hasPublicationYear "2022" @default.
• W4214899414 type Work @default.
• W4214899414 citedByCount "1" @default.
• W4214899414 countsByYear W42148994142023 @default.
• W4214899414 crossrefType "journal-article" @default.
• W4214899414 hasAuthorship W4214899414A5001620324 @default.
• W4214899414 hasAuthorship W4214899414A5083867120 @default.
• W4214899414 hasConcept C110729354 @default.
• W4214899414 hasConcept C114614502 @default.
• W4214899414 hasConcept C121332964 @default.
• W4214899414 hasConcept C134306372 @default.
• W4214899414 hasConcept C33923547 @default.
• W4214899414 hasConcept C99730327 @default.
• W4214899414 hasConceptScore W4214899414C110729354 @default.
• W4214899414 hasConceptScore W4214899414C114614502 @default.
• W4214899414 hasConceptScore W4214899414C121332964 @default.
• W4214899414 hasConceptScore W4214899414C134306372 @default.
• W4214899414 hasConceptScore W4214899414C33923547 @default.
• W4214899414 hasConceptScore W4214899414C99730327 @default.
• W4214899414 hasFunder F4320321001 @default.
• W4214899414 hasFunder F4320322769 @default.
• W4214899414 hasIssue "3" @default.
• W4214899414 hasLocation W42148994141 @default.
• W4214899414 hasOpenAccess W4214899414 @default.
• W4214899414 hasPrimaryLocation W42148994141 @default.
• W4214899414 hasRelatedWork W1916943071 @default.
• W4214899414 hasRelatedWork W1973865997 @default.
• W4214899414 hasRelatedWork W1985684185 @default.
• W4214899414 hasRelatedWork W2121711034 @default.
• W4214899414 hasRelatedWork W2136017802 @default.
• W4214899414 hasRelatedWork W2329865134 @default.
• W4214899414 hasRelatedWork W2963375143 @default.
• W4214899414 hasRelatedWork W4253570894 @default.
• W4214899414 hasRelatedWork W2604017320 @default.
• W4214899414 hasRelatedWork W3100109466 @default.
• W4214899414 hasVolume "34" @default.
• W4214899414 isParatext "false" @default.
• W4214899414 isRetracted "false" @default.
• W4214899414 workType "article" @default.