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Asymptotics for solutions of elliptic equations in double divergence form
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
North Eastern University.
2007 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, Vol. 32, no 2, 191-207 p.Article in journal (Refereed) Published
Abstract [en]

We consider weak solutions of an elliptic equation of the form ∂i∂i(aiju) = 0 and their asymptotic properties at an interior point. We assume that the coefficients are bounded, measurable, complex-valued functions that stabilize as x → 0 in that the norm of the matrix (aij(x) - δij) on the annulus B2r\Br is bounded by a function Ω(r), where Ω2(r) satisfies the Dini condition at r = 0, as well as some technical monotonicity conditions, under these assumptions, solutions need not be continuous. Our main result is an explicit formula for the leading asymptotic term for solutions with at most a mild singularity at x = 0. As a consequence, we obtain upper and lower estimates for the Lp-norm of solutions, as well as necessary and sufficient conditions for solutions to be bounded or tend to zero in Lp-mean as r → 0. Copyright © Taylor & Francis Group, LLC.

Place, publisher, year, edition, pages
2007. Vol. 32, no 2, 191-207 p.
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URN: urn:nbn:se:liu:diva-40052DOI: 10.1080/03605300601113019Local ID: 52192OAI: diva2:260901
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-11

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Maz´ya, Vladimir G.
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The Institute of TechnologyApplied Mathematics
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