# The Dirichlet problem in convex bounded domains for operators in non-divergence form with L?-coefficients

Hieber, Matthias, Wood, Ian (2007) The Dirichlet problem in convex bounded domains for operators in non-divergence form with L?-coefficients. Differential Integral Equations, 20 (7). pp. 721-734. ISSN 0893-4983. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:44243)

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## Abstract

Consider the Dirichlet problem for elliptic and parabolic equations in nondivergence form

elliptic problem and maximal

the coefficients $a_{ij} \in L^\infty$ 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.

Item Type: Article Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Ian Wood 10 Nov 2014 18:01 UTC 16 Feb 2021 12:57 UTC https://kar.kent.ac.uk/id/eprint/44243 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-7181-7075