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The Dirichlet problem for second order parabolic operators in divergence form
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)Article in journal (Refereed) Submitted
Abstract [en]

We study parabolic operators $\cH = \partial_t-\div_{\lambda,x} A(x,t)\nabla_{\lambda,x}$ in the parabolic upper half space $\mathbb R^{n+2}_+=\{(\lambda,x,t):\ \lambda>0\}$. We assume that the coefficients are real, bounded, measurable, uniformly elliptic, but not necessarily symmetric. We prove that the associated parabolic measure is  absolutely continuous with respect to the surface measure on $\mathbb R^{n+1}$  in the sense defined by $A_\infty(\mathrm{d} x\d t)$. Our argument also gives a simplified proof of the corresponding result for elliptic measure.

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URN: urn:nbn:se:uu:diva-306716OAI: oai:DiVA.org:uu-306716DiVA: diva2:1044316
Available from: 2016-11-02 Created: 2016-11-02 Last updated: 2017-02-21

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Nyström, Kaj
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