### Abstract

The property of maximal L_{p}-regularity for parabolic evolution equations is investigated via the concept of R-sectorial operators and operator-valued Fourier multipliers. As application, we consider the L _{q}-realization of an elliptic boundary value problem of order 2m with operator-valued coefficients subject to general boundary conditions. We show that there is maximal L_{p}-L_{q}-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Original language | English |
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Journal | Memoirs of the American Mathematical Society |

Issue number | 788 |

Publication status | Published - 2003 Nov |

Externally published | Yes |

### Keywords

- Differential operators with operator-valued coefficients
- L-theory for boundary value problems of general type
- Lopatinskii-Shapiro condition
- Maximal L-regularity
- Operator-valued Fourier multipliers
- R-boundedness

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Denk, R., Hieber, M. G., & Prüss, J. (2003). R-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type.

*Memoirs of the American Mathematical Society*, (788).