The Dirichlet problem in convex bounded domains for operators with L^\infty-coefficients
Contribuinte(s) |
Institute of Mathematics & Physics (ADT) Mathematics and Physics |
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Data(s) |
05/12/2007
05/12/2007
2007
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Resumo |
M.Hieber, I.Wood: The Dirichlet problem in convex bounded domains for operators with L^\infty-coefficients, Diff. Int. Eq., 20, 7 (2007),721-734. Consider the Dirichlet problem for elliptic and parabolic equations in nondivergence form with variable coefficients in convex bounded domains of R^n. We prove solvability of the elliptic problem and maximal L^q-L^p-estimates for the solution of the parabolic problem provided the coefficients are bounded, satisfy a Cordes condition and p in (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 in (1,2] is close to 2, for maximal L^q-L^p-regularity in the parabolic case an additional assumption on the growth of the coefficients is needed. Peer reviewed |
Formato |
14 |
Identificador |
Wood , I & Hieber , M 2007 , ' The Dirichlet problem in convex bounded domains for operators with L^\infty-coefficients ' Differential and Integral Equations , vol 20 , no. 7 , pp. 721-734 . 0893-4983 PURE: 72906 PURE UUID: 03f837f8-3931-4fcc-b731-7bbd49917eef dspace: 2160/390 |
Idioma(s) |
eng |
Relação |
Differential and Integral Equations |
Tipo |
/dk/atira/pure/researchoutput/researchoutputtypes/contributiontojournal/article Article (Journal) |
Direitos |