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Pathological solutions to elliptic problems in divergence form with continuous coefficients
Rutgers State University.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Univ Catholique Louvain.
2009 (English)In: COMPTES RENDUS MATHEMATIQUE, ISSN 1631-073X, Vol. 347, no 13-14, 773-778 p.Article in journal (Refereed) Published
Abstract [en]

We construct a function u is an element of W-loc(1.1) (B(0, 1)) which is a solution to div(A del u) = 0 in the sense of distributions, where A is continuous and u is not an element of W-loc(1.p) (B(0, 1)) for p greater than 1. We also give a function u is an element of W-loc(1.1)(B(0, 1)) such that u is an element of W-loc(1.p) (B(0, 1)) for every p less than infinity, u satisfies div(A del u) = 0 with A continuous but u is not an element of W-loc(1.infinity) (B(0, 1)). This answers questions raised by H. Brezis (On a conjecture of J. Serrin, Rend. Lincei Mat. Appl. 19 (2008) 335-338).

Place, publisher, year, edition, pages
2009. Vol. 347, no 13-14, 773-778 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-20145DOI: 10.1016/j.crma.2009.05.008OAI: oai:DiVA.org:liu-20145DiVA: diva2:233658
Available from: 2009-09-01 Created: 2009-08-31 Last updated: 2009-09-01

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Mazya, Vladimir

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