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Regularity of solutions to the polyharmonic equation in general domains
University of Minnesota, MN 55408 USA .
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 196, no 1, 0464- p.Article in journal (Refereed) Published
Abstract [en]

The present paper establishes boundedness of derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of , 2a parts per thousand currency signna parts per thousand currency sign2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.

Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2014. Vol. 196, no 1, 0464- p.
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-106126DOI: 10.1007/s00222-013-0464-1ISI: 000333160600001OAI: diva2:714041
Available from: 2014-04-25 Created: 2014-04-24 Last updated: 2014-04-25

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Maz´ya, Vladimir
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Mathematics and Applied MathematicsThe Institute of Technology
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