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Extension properties and boundary estimates for a fractional heat operator
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.
2016 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 140, 29-37 p.Article in journal (Refereed) Published
##### Abstract [en]

The square root of the heat operator $\sqrt{\partial_t-\Delta}$, can be realized as the Dirichlet to Neumann map of the heat extension of data on $\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar characterizations for general fractional powers of the heat operator, $(\partial_t-\Delta)^s$, $s\in (0,1)$. Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.

##### Place, publisher, year, edition, pages
2016. Vol. 140, 29-37 p.
Mathematics
##### Identifiers
ISI: 000375484000003OAI: oai:DiVA.org:uu-266836DiVA: diva2:868830
Available from: 2015-11-11 Created: 2015-11-11 Last updated: 2016-06-29Bibliographically approved

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