Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Field sensitivity to L^p variations of a scatterer   For the problem of diffraction of harmonic scalar waves by a lossless
periodic slab scatterer, we analyze field sensitivity with respect to the
material coefficients of the slab. The governing equation is the Helmholtz
equation, which describes acoustic or electromagnetic fields. The main theorem
establishes the variational Frechet derivative of the scattered field measured
in the H^1 (root-mean-square-gradient) norm as a function of the material
coefficients measured in an L^p (p-power integral) norm, with 2<p<infinity, as
long as these coefficients are bounded above and below by positive constants
and do not admit resonance. The derivative is Lipschitz continuous. We also
establish the variational derivative of the transmitted energy with respect to
the material coefficients in L^p.

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The categories of this paper are: atom-ph
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas