Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary unique continuation on $C^1$-Dini domains and the size of the
  singular set   Let $u$ be a harmonic function in a $C^1$-Dini domain $D$ such that $u$
vanishes on a boundary surface ball $\partial D \cap B_{5R}(0)$. We consider an
effective version of its singular set (up to boundary) $\mathcal{S}(u):=\{X\in
\overline{D}: u(X) = |\nabla u(X)| = 0\} $ and give an estimate of its
$(d-2)$-dimensional Minkowski content, which only depends on the upper bound of
some modified frequency function of $u$ centered at $0$. Such results are
already known in the interior and at the boundary of convex domains, when the
standard frequency function is monotone at every point. The novelty of our work
on Dini domains is how to compensate for the lack of such monotone quantities
at boundary as well as interior points.

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The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas