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Maximal L p -regularity for a linear three-phase problem of parabolic–elliptic type

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2010

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http://nbn-resolving.de/urn:nbn:de:bsz:352-255010
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https://doi.org/10.1007/s00028-009-0050-6
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Journal of Evolution Equations. 2010, 10(2), pp. 293-318. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-009-0050-6

Zusammenfassung

We prove maximal L p -regularity for a three-phase problem consisting of strongly coupled parabolic–elliptic equations with inhomogeneous data. This problem is related to a nonlinear problem which arises in chemically reacting systems incorporating electromigration. Particular features are a transmission condition and a jump condition on the boundary, which couple all unknowns. By means of localization the problem is reduced to model problems in full and half-space. To solve model problems, we make use of Dore–Venni Theory, real interpolation and the Mikhlin multiplier theorem in the operator-valued version. Here it is crucial to find conditions on the data that are necessary and sufficient for maximal L p -regularity of the respective solution.

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510 Mathematik

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ISO 690KOTSCHOTE, Matthias, 2010. Maximal L p -regularity for a linear three-phase problem of parabolic–elliptic type. In: Journal of Evolution Equations. 2010, 10(2), pp. 293-318. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-009-0050-6
BibTex
@article{Kotschote2010Maxim-25501,
  year={2010},
  doi={10.1007/s00028-009-0050-6},
  title={Maximal L <sub>p</sub> -regularity for a linear three-phase problem of parabolic–elliptic type},
  number={2},
  volume={10},
  issn={1424-3199},
  journal={Journal of Evolution Equations},
  pages={293--318},
  author={Kotschote, Matthias}
}
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