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New weighted inequalities with applications to pseudodifferential operators
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology. Univ.,.
2001 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is devoted to weighted integral inequalities and their applications to the  study of boundary behavior of solutions to Dirichlet's problem for fractional powers of the Laplacian.

We obtain a necessary and sufficient condition on μ for the operator (—Δ)μin R 0 , 0 < μ < n/2 to have the so called weighted positivity property, the weight being the fundamental solution of the operator. This property is also studied for ordinary differential operators and we provide various examples of operators with and without the property.

The optimal constants in a two parameter family of Hardy-Rellich type inequalities are found. A number of other weighted inequalities related to fractional derivative are obtained.

A sufficient Wiener type condition for regularity of a boundary point with respect to (-,;:.)μ is obtained for the range of μ ensuring the weighted positivity property. For the same μ's, we also study the behavior of the μ-harmonic Dirichlet capacitary

potential near a boundary point which do not satisfy the Wiener condition

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2001. , p. 81
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 692
Keyword [en]
Weighted integral inequalities, fractional Laplacian, Dirichlet problem, behavior near the boundary, special functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-143536ISBN: 9173730327 (print)OAI: oai:DiVA.org:liu-143536DiVA: diva2:1164789
Public defence
2001-05-23, BL32, hus B bv, ingång 23, Campus Valla, Linköping, 10:15 (English)
Opponent
Available from: 2017-12-12 Created: 2017-12-12 Last updated: 2018-01-08Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
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  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf