Boundary value problems for parabolic systems via a first order approach
2016 (English)Article in journal (Refereed) Submitted
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.
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IdentifiersURN: urn:nbn:se:uu:diva-300486OAI: oai:DiVA.org:uu-300486DiVA: diva2:951498