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2012 Weighted maximal regularity estimates and solvability of nonsmooth elliptic systems, II
Pascal Auscher, Andreas Rosén
Anal. PDE 5(5): 983-1061 (2012). DOI: 10.2140/apde.2012.5.983

Abstract

We continue the development, by reduction to a first-order system for the conormal gradient, of L2 a priori estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence-form second-order complex elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning a priori almost everywhere nontangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying a posteriori a separate work on bounded domains.

Citation

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Pascal Auscher. Andreas Rosén. "Weighted maximal regularity estimates and solvability of nonsmooth elliptic systems, II." Anal. PDE 5 (5) 983 - 1061, 2012. https://doi.org/10.2140/apde.2012.5.983

Information

Received: 23 January 2011; Accepted: 18 November 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1275.35093
MathSciNet: MR3022848
Digital Object Identifier: 10.2140/apde.2012.5.983

Subjects:
Primary: 35J25, 35J55, 35J56, 35J57, 42B25

Rights: Copyright © 2012 Mathematical Sciences Publishers

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