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A backward in time Harnack inequality for non-negative solutions to fully non-linear parabolic equations
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2014 (English)In: Revista di Matematica della Universita Di Parma, ISSN 0035-6298, Vol. 5, no 1, 1-14 p.Article in journal (Refereed) Published
Abstract [en]

We consider fully non-linear parabolic equations of the form\[Hu =F(D^2u(x,t),Du(x,t),x,t)-\partial_tu = 0\]in bounded space-time domains $D\subset\mathbb R^{n+1}$, assuming only $F(0,0,x,t)=0$ and a uniform parbolicity condition on $F$. For domains of the form $\Omega_T=\Omega\times (0,T)$, where $\Omega\subset\mathbb R^n$ is a bounded Lipschitz and $T>0$, we establish a scale-invariant backward in time Harnackinequality for non-negative solutions vanishing on the lateral boundary. Our argument rests on the comparison principle, the Harnack inequality and local H{\"o}lder continuity estimates.

Place, publisher, year, edition, pages
2014. Vol. 5, no 1, 1-14 p.
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URN: urn:nbn:se:uu:diva-204866OAI: oai:DiVA.org:uu-204866DiVA: diva2:639978
Available from: 2013-08-12 Created: 2013-08-12 Last updated: 2016-04-13Bibliographically approved

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