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

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. (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)

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. (Contact us about this Publication)

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)
  • Depositors only (login required):