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L2 well-posedness of boundary value problems and the Kato square root problem for parabolic systems with measurable coefficients
Univ. Paris-Sud, CNRS, Universit´e Paris-Saclay.
Univ. Paris-Sud, CNRS, Universit´e Paris-Saclay.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863Article in journal (Refereed) Accepted
Abstract [en]

We introduce a first order strategy to study boundary value problems of parabolic systems with second order elliptic part in the upper half-space. This involves a parabolic Dirac operator at the boundary. We allow for measurable time dependence and some transversal dependence in the coefficients. We obtain layer potential representations for solutions in some classes and prove new well-posedness and perturbation results. As a byproduct, we prove for the first time a Kato estimate for the square root of parabolic operators with time dependent coefficients. This considerably extends prior results obtained by one of us under time and transversal independence. A major difficulty compared to a similar treatment of elliptic equations is the presence of non-local fractional derivatives in time.

Place, publisher, year, edition, pages
2016.
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Mathematics
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URN: urn:nbn:se:uu:diva-300486OAI: oai:DiVA.org:uu-300486DiVA, id: diva2:951498
Available from: 2016-08-09 Created: 2016-08-09 Last updated: 2018-03-10

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Nyström, Kaj

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