Abstract
The property of maximal Lp-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 Lp-Lq-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
| Original language | English |
|---|---|
| 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)