Hieber, Matthias and 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.
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## Abstract

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 $a_{ij} \in L^\infty$ 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 |
---|---|

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Faculties > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 10 Nov 2014 18:01 UTC |

Last Modified: | 10 Nov 2014 18:01 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/44243 (The current URI for this page, for reference purposes) |

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