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

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

Type of Publication: Journal article
Author: Kotschote, Matthias
Year of publication: 2010
Published in: Journal of Evolution Equations ; 10 (2010), 2. - pp. 293-318. - ISSN 1424-3199. - eISSN 1424-3202
DOI (citable link): https://dx.doi.org/10.1007/s00028-009-0050-6
Summary:
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.
Subject (DDC): 510 Mathematics
Bibliography of Konstanz: Yes

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KOTSCHOTE, Matthias, 2010. Maximal L p -regularity for a linear three-phase problem of parabolic–elliptic type. In: Journal of Evolution Equations. 10(2), pp. 293-318. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-009-0050-6

@article{Kotschote2010Maxim-25501, title={Maximal L p -regularity for a linear three-phase problem of parabolic–elliptic type}, year={2010}, doi={10.1007/s00028-009-0050-6}, number={2}, volume={10}, issn={1424-3199}, journal={Journal of Evolution Equations}, pages={293--318}, author={Kotschote, Matthias} }

2010 Journal of Evolution Equations ; 10 (2010), 2. - S. 293-318 terms-of-use Kotschote, Matthias Kotschote, Matthias 2013-12-18T08:08:44Z 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. 2013-12-18T08:08:44Z eng Maximal L <sub>p</sub> -regularity for a linear three-phase problem of parabolic–elliptic type

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