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Symmetrization of exterior parabolic problems and probabilistic interpretation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2017 (English)In: STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, ISSN 2194-0401, Vol. 5, no 1, 38-52 p.Article in journal (Refereed) Published
Abstract [en]

We prove a comparison theorem for the spatial mass of the solutions of two exterior parabolic problems, one of them having symmetrized geometry, using approximation of the Schwarz symmetrization by polarizations, as it was introduced in Brock and Solynin (TransAmMath Soc 352(4): 1759-1796, 2000). This comparison provides an alternative proof, based on PDEs, of the isoperimetric inequality for the Wiener sausage, which was proved in Peres and Sousi (Geom Funct Anal 22(4): 10001014, 2012).

Place, publisher, year, edition, pages
SPRINGER , 2017. Vol. 5, no 1, 38-52 p.
Keyword [en]
Schwarz symmetrization, Polarization, Parabolic equations, Wiener sausage
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-333417DOI: 10.1007/s40072-016-0080-3ISI: 000406353300002OAI: oai:DiVA.org:uu-333417DiVA: diva2:1156544
Available from: 2017-11-13 Created: 2017-11-13 Last updated: 2017-11-13Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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