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Type of Publication:  Journal article 
Author:  Kotschote, Matthias 
Year of publication:  2010 
Published in:  Journal of Evolution Equations ; 10 (2010), 2.  pp. 293318.  ISSN 14243199.  eISSN 14243202 
DOI (citable link):  https://dx.doi.org/10.1007/s0002800900506 
Summary: 
We prove maximal L p regularity for a threephase 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 halfspace. To solve model problems, we make use of Dore–Venni Theory, real interpolation and the Mikhlin multiplier theorem in the operatorvalued 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 threephase problem of parabolic–elliptic type. In: Journal of Evolution Equations. 10(2), pp. 293318. ISSN 14243199. eISSN 14243202. Available under: doi: 10.1007/s0002800900506
@article{Kotschote2010Maxim25501, title={Maximal L _{p} regularity for a linear threephase problem of parabolic–elliptic type}, year={2010}, doi={10.1007/s0002800900506}, number={2}, volume={10}, issn={14243199}, journal={Journal of Evolution Equations}, pages={293318}, author={Kotschote, Matthias} }