Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The L^p Dirichlet Problem and Nondivergence Harmonic Measure   We consider the Dirichlet problem Lu = 0 in D u = g on E = boundary of D for
two second order elliptic operators L_k(u) = \sum_{i,j=1}^n a_k^{ij}(x)
\partial_{ij} u(x), k=0,1, in a bounded Lipschitz domain D in R^n. The
coefficients a_k^{ij} belong to the space of bounded mean oscillation BMO with
a suitable small BMO modulus. We assume that L_0 is regular in L^p(E,ds) for
some p, 1<p<\infty, that is, |Nu|_{L^p}< C |g|_{L^p} for all continuous
boundary data g. Here ds is the surface measure on E and Nu is the
nontangential maximal operator. The aim of this paper is to establish
sufficient conditions on the difference of the coefficients
a_1^{ij}(x)-a_0^{ij}(x) that will assure the perturbed operator L_1 to be
regular in L^q(E,ds) for some q, 1<q<\infty.

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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: eess
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: cs