R-Boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type (Memoirs of the American Mathematical Society) - Softcover

Denk, Robert; Hieber, Matthias; Pruss, Jan

Softcover

ISBN 10: 0821833782 ISBN 13: 9780821833780

Publisher: Amer Mathematical Society, 2003

Synopsis

The property of maximal $Lp$-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 $Lq$-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 $Lp$-$Lq$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 2003
• ISBN 10: 0821833782
• ISBN 13: 9780821833780
• Binding: Paperback
• Language: English
• Number of pages: 114