Inhomogeneous symbols, the Newton polygon, and maximal Lp-regularity

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2008
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https://doi.org/10.1134/S1061920808020040
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Russian Journal of Mathematical Physics. Springer. 2008, 15(2), pp. 171-191. ISSN 1061-9208. eISSN 1555-6638. Available under: doi: 10.1134/S1061920808020040
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We prove a maximal regularity result for operators corresponding to rotation invariant symbols (in space) which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary-value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on the H∞-calculus and R-bounded operator families. As an application, we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction.

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510 Mathematik
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ISO 690DENK, Robert, Jürgen SAAL, Jörg SEILER, 2008. Inhomogeneous symbols, the Newton polygon, and maximal Lp-regularity. In: Russian Journal of Mathematical Physics. Springer. 2008, 15(2), pp. 171-191. ISSN 1061-9208. eISSN 1555-6638. Available under: doi: 10.1134/S1061920808020040
BibTex
@article{Denk2008Inhom-524.2,
  year={2008},
  doi={10.1134/S1061920808020040},
  title={Inhomogeneous symbols, the Newton polygon, and maximal L<sup>p</sup>-regularity},
  number={2},
  volume={15},
  issn={1061-9208},
  journal={Russian Journal of Mathematical Physics},
  pages={171--191},
  author={Denk, Robert and Saal, Jürgen and Seiler, Jörg}
}
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