Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lecture notes on quantitative unique continuation for solutions of
  second order elliptic equations   In these lectures we present some useful techniques to study quantitative
properties of solutions of elliptic PDEs. Our aim is to outline a proof of a
recent result on propagation of smallness. The ideas are also useful in the
study of the zero sets of eigenfunctions of Laplace-Beltrami operator and we
discuss the connection. Some basic facts about second order elliptic PDEs in
divergent form are collected in the Appendix at the end of the notes.

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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc