Maximal L_p-regularity for a linear three-phase problem of parabolic¨Celliptic type

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• 作者：Matthias Kotschote
• 关键词：Maximal regularity ; Parabolic– ; elliptic systems ; Electroneutrality ; RH£¤{{\mathcal R}{\mathcal H}^\infty} ; calculus ; Operator ; valued Fourier multipliers ; Inhomogeneous boundary conditions
• 刊名：Journal of Evolution Equations
• 出版年：2010
• 出版时间：May, 2010
• 年：2010
• 卷：10
• 期：2
• 页码：293-318
• 全文大小：333.4 KB

文摘

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.