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Weighted maximal regularity estimates and solvability of non-smooth elliptic systems, II
Département de Mathématiques d’Orsay, Université Paris-Sud et UMR 8628 du CNRS, Orsay Cedex, France.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2012 (English)In: Analysis & PDE, ISSN 2157-5045, Vol. 5, no 5, 983-1061 p.Article in journal (Refereed) Published
Abstract [en]

We continue the development, by reduction to a first-order system for the conormal gradient, of L2a 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.

Place, publisher, year, edition, pages
Mathematical Sciences Publishers , 2012. Vol. 5, no 5, 983-1061 p.
Keyword [en]
elliptic system, conjugate function, maximal regularity, Dirichlet and Neumann problems, square function, nontangential maximal function, functional and operational calculus, Fredholm theory
National Category
Mathematical Analysis
URN: urn:nbn:se:liu:diva-89305DOI: 10.2140/apde.2012.5.983ISI: 000318401200004OAI: diva2:607675
Available from: 2013-02-25 Created: 2013-02-25 Last updated: 2013-06-11

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Rosén, Andreas
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Mathematics and Applied MathematicsThe Institute of Technology
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