DOI
10.1007/s00028-011-0133-z
Abstract
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is satisfied in the setting of periodic little-Hölder spaces, provided the coefficients of the differential operator satisfy minimal regularity assumptions.We address parameter-dependent elliptic equations, deriving invertibility and resolvent bounds which lead to results on generation of analytic semigroups. We also demonstrate that the techniques and results of the paper hold for elliptic differential operators with operator-valued coefficients, in the setting of vector-valued functions.
Document Type
Post-print Article
Publication Date
12-10-2011
Publisher Statement
Copyright © 2011, Springer Basel AG. Article first published online: December 10, 2011
The definitive version is available at: http://link.springer.com/article/10.1007/s00028-011-0133-z
DOI: 10.1007/s00028-011-0133-z
Full Citation:
Lecrone, Jeremy. "Elliptic Operators and Maximal Regularity on Periodic Little-Hölder Spaces." Journal of Evolution Equations 12, no. 2 (2011): 295-325. doi:10.1007/s00028-011-0133-z.
Recommended Citation
LeCrone, Jeremy, "Elliptic operators and maximal regularity on periodic little-Hölder spaces" (2011). Department of Math & Statistics Faculty Publications. 161.
https://scholarship.richmond.edu/mathcs-faculty-publications/161