R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type
著者
書誌事項
R-boundedness, Fourier multipliers, and problems of elliptic and parabolic type
（Memoirs of the American Mathematical Society, no. 788）
American Mathematical Society, 2003
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注記
"Volume 166, number 788 (first of 3 numbers)."
Includes bibliographical references (p. 111-114)
内容説明・目次
内容説明
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.
目次
- Introduction Notations and conventions $\mathcal R$-Boundedness and Sectorial Operators: Sectorial operators The classes ${\mathcal{BIP}}(X)$ and $\mathcal H^\infty(X)$ $\mathcal R$-bounded families of operators $\mathcal R$-sectorial operators and maximal $L_p$-regularity Elliptic and Parabolic Boundary Value Problems: Elliptic differential operators in $L_p(\mathbb{R}^n
- E)$ Elliptic problems in a half space: General Banach spaces Elliptic problems in a half space: Banach spaces of class $\mathcal{HT}$ Elliptic and parabolic problems in domains Notes References.
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