$\mathcal {R}$-Boundedness, Fourier Multipliers and Problems of Elliptic and Parabolic Type
Robert Denk · Matthias Hieber · Jan Prüss
Jan 2003 · American Mathematical Soc.
Ebook
114
Pages
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About this ebook
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-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.
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