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Boundary behavior of solutions to the parabolic p-Laplace equation
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)Article in journal (Refereed) Submitted
Abstract [en]

We establish boundary estimates for non-negative solutions to the $p$-parabolic equation in the degenerate range $p>2$. Our main results include new parabolic intrinsic Harnack chains in cylindrical NTA-domains together with sharp boundary decay estimates. If the underlying domain is $C^{1,1}$-regular, we establish a relatively complete theory of the boundary behavior, including boundary Harnack principles and H\"older continuity of the ratios of two solutions, as well as fine properties of associated boundary measures. There is an intrinsic waiting time phenomena present which plays a fundamental role throughout the paper. In particular, conditions on these waiting times rule out well-known examples of explicit solutions violating the boundary Harnack principle.

Place, publisher, year, edition, pages
2015.
National Category
Mathematics
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URN: urn:nbn:se:uu:diva-265500OAI: oai:DiVA.org:uu-265500DiVA, id: diva2:865965
Available from: 2015-10-30 Created: 2015-10-30 Last updated: 2016-02-17Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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