Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted maximal regularity estimates and solvability of non-smooth
  elliptic systems II   We continue the development, by reduction to a first order system for the
conormal gradient, of $L^2$ \textit{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 \textit{a priori} almost everywhere non-tangential
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 \textit{a posteriori} a separate work
on bounded domains.

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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph