Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on quantitative unique continuation from subsets of the
  boundary of positive measure   The question of unique continuation of harmonic functions in a domain
$\Omega$ $\subset$ R d with boundary $\partial$$\Omega$, satisfying Dirichlet
boundary conditions and with normal derivatives vanishing on a subset $\omega$
of the boundary is a classical problem. When $\omega$ contains an open subset
of the boundary it is a consequence of Carleman estimates (uniqueness for
second order elliptic operators across an hypersurface). The case where
$\omega$ is a set of positive (d -- 1) dimensional measure has attracted a lot
of attention, see e.g. [10, 3, 15], where qualitative results have been
obtained in various situations. The main open questions (about uniqueness)
concern now Lipschitz domains and variable coefficients. Here, using results by
Logunov and Malinnikova [13, 14], we consider the simpler case of W 2,$\infty$
domains but prove quantitative uniqueness both for Dirichlet and Neumann
boundary conditions. As an application, we deduce quantitative estimates for
the Dirichlet and Neumann Laplace eigenfunctions on a W 2,$\infty$ domain with
boundary.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th