Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of Fourier analysis in homogenization of Dirichlet problem
  I. Pointwise Estimates   In this paper we prove convergence results for homogenization problem for
solutions of partial differential system with rapidly oscillating Dirichlet
data. Our method is based on analysis of oscillatory integrals. In the
uniformly convex and smooth domain, and smooth operator and boundary data, we
prove pointwise convergence results, namely $$|u_{\e}(x)-u_0 (x)| \leq
C_{\kappa} \e^{(d-1)/2}\frac{1}{d(x)^{\kappa}}, \ \forall x\in D, \ \forall \
\kappa>d-1,$$ where $u_{\e}$ and $u_0$ are solutions of respectively
oscillating and homogenized Dirichlet problems, and $d(x)$ is the distance of
$x$ from the boundary of $D$. As a corollary for all $1\leq p <\infty$ we
obtain $L^p$ convergence rate as well.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an