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On time dependent domains for the degenerate p-parabolic equation: Carleson estimate and Holder continuity
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Univ Jyvaskyla, Dept Math & Stat, POB 35, Jyvaskyla 40014, Finland.;Aalto Univ, Inst Math, POB 11100, Aalto 00076, Finland..
2016 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 364, no 1-2, 667-686 p.Article in journal (Refereed) PublishedText
Abstract [en]

In this paper we propose a definition of "parabolic NTA" for solutions to the degenerate p-parabolic equation. Given this definition we prove the Carleson estimate, originally proved for this equation in Avelin et al. (J Eur Math Soc, 2015) for cylindrical domains. Moreover we study a non-optimal, stronger "outer corkscrew" condition, such that we obtain Holder continuity up to the boundary, for non-negative solutions vanishing on a part of the boundary.

Place, publisher, year, edition, pages
2016. Vol. 364, no 1-2, 667-686 p.
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URN: urn:nbn:se:uu:diva-298255DOI: 10.1007/s00208-015-1226-8ISI: 000376064900024OAI: oai:DiVA.org:uu-298255DiVA: diva2:945291
Available from: 2016-07-01 Created: 2016-07-01 Last updated: 2016-07-01Bibliographically approved

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