Memoirs of the American Mathematical Society 2003; 114 pp; softcover Volume: 166 ISBN10: 0821833782 ISBN13: 9780821833780 List Price: US$61 Individual Members: US$36.60 Institutional Members: US$48.80 Order Code: MEMO/166/788
 The property of maximal \(L_p\)regularity for parabolic evolution equations is investigated via the concept of \(\mathcal R\)sectorial operators and operatorvalued Fourier multipliers. As application, we consider the \(L_q\)realization of an elliptic boundary value problem of order \(2m\) with operatorvalued 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. Readership Graduate students and research mathematicians interested in differential equations. Table of Contents  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
