Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local wellposedness of quasilinear Maxwell equations with conservative
  interface conditions   We establish a comprehensive local wellposedness theory for the quasilinear
Maxwell system with interfaces in the space of piecewise $H^m$-functions for $m
\geq 3$. The system is equipped with instantaneous and piecewise regular
material laws and perfectly conducting interfaces and boundaries. We also
provide a blow-up criterion in the Lipschitz norm and prove the continuous
dependence on the data. The proof relies on precise a priori estimates and the
regularity theory for the corresponding linear problem also shown here.

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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas