The Dirichlet problem in convex bounded domains for operators with L8-coefficients

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dc.contributor.author Hieber, Matthias
dc.contributor.author Wood, Ian
dc.date.accessioned 2008-12-05T11:17:51Z
dc.date.available 2008-12-05T11:17:51Z
dc.date.issued 2007-07-01
dc.identifier.citation Hieber , M & Wood , I 2007 , ' The Dirichlet problem in convex bounded domains for operators with L8-coefficients ' Differential and Integral Equations , vol 20 , no. 7 , pp. 721-734 . en
dc.identifier.issn 0893-4983
dc.identifier.other PURE: 88760
dc.identifier.other dspace: 2160/1413
dc.identifier.uri http://hdl.handle.net/2160/1413
dc.identifier.uri http://projecteuclid.org/euclid.die/1356039406 en
dc.description Wood, Ian; Hieber, M., (2007) 'The Dirichlet problem in convex bounded domains for operators with L8-coefficients', Differential and Integral Equations 20 pp.721-734 RAE2008 en
dc.description.abstract Consider the Dirichlet problem for elliptic and parabolic equations in non-divergence form with variable coefficients in convex bounded domains of Rn. We prove solvability of the elliptic problem and maximal Lq-Lp-estimates for the solution of the parabolic problem provided the coefficients aij∈L∞ satisfy a Cordes condition and p∈(1,2] is close to 2. This implies that in two dimensions, i.e., n=2, the elliptic Dirichlet problem is always solvable if the associated operator is uniformly strongly elliptic, and p∈(1,2] is close to 2, for maximal Lq-Lp-regularity in the parabolic case an additional assumption on the growth of the coefficients is needed. en
dc.format.extent 14 en
dc.language.iso eng
dc.relation.ispartof Differential and Integral Equations en
dc.title The Dirichlet problem in convex bounded domains for operators with L8-coefficients en
dc.type Text en
dc.type.publicationtype Article (Journal) en
dc.contributor.institution Institute of Mathematics & Physics (ADT) en
dc.contributor.institution Mathematics and Physics en
dc.description.status Peer reviewed en


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