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.
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
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.
LeCrone, Jeremy, "Elliptic operators and maximal regularity on periodic little-Hölder spaces" (2011). Math and Computer Science Faculty Publications. 161.