Mathematics – Analysis of PDEs
Scientific paper
2006-07-28
Mathematics
Analysis of PDEs
21 pages
Scientific paper
It is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators of a bundle of Banach spaces of class (HT) and Pisier's property $(\alpha)$ has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of $A$ on the scattering cotangent bundle of the manifold avoids the right half-plane. This is deduced directly from a Seeley theorem, i.e. the resolvent is represented in terms of pseudodifferential operators with R-bounded symbols, thus showing by an iteration argument the R-boundedness of $\lambda(A-\lambda)^{-1}$ for $\Re(\lambda) \geq 0$. To this end, elements of a symbolic and operator calculus of pseudodifferential operators with R-bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on $R^d$ with operator valued coefficients.
Denk Robert
Krainer Thomas
No associations
LandOfFree
R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-251353