Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenization of a parabolic Dirichlet problem by a method of Dahlberg   Consider the linear parabolic operator in divergence form $$\mathcal{H} u
=\partial_t u(X,t)-\text{div}(A(X)\nabla u(X,t)).$$ We employ a method of
Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half
plane is well-posed for boundary data in $L^p$, for any elliptic matrix of
coefficients $A$ which is periodic and satisfies a Dini-type condition. This
result allows us to treat a homogenization problem for the equation $\partial_t
u_\varepsilon(X,t)-\text{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in
Lipschitz domains with $L^p$-boundary data.

4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an