The Dirichlet problem in convex bounded domains for operators with L8-coefficients
Contribuinte(s) |
Institute of Mathematics & Physics (ADT) Mathematics and Physics |
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Data(s) |
05/12/2008
05/12/2008
01/07/2007
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Resumo |
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 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. Peer reviewed |
Formato |
14 |
Identificador |
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 . 0893-4983 PURE: 88760 PURE UUID: cde2b36e-9cbe-489a-ba5b-25040caa9483 dspace: 2160/1413 |
Idioma(s) |
eng |
Relação |
Differential and Integral Equations |
Tipo |
/dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article Article (Journal) |
Direitos |