Maximal $L_p$-regularity of non-local boundary value problems

Abstract

We investigate the $\mathcal{R}$-boundedness of operator families belonging to the Boutet de Monvel calculus. In particular, we show that weakly and strongly parameter-dependent Green operators of nonpositive order are $\mathcal{R}$-bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems. As a consequence, we obtain maximal $L_p$-regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.

References in corpus (1)

• Bounded ${\mathbf{H}}_{\infty }$-Calculus for Differential Operators on Conic Manifolds with Boundary

Cited by in corpus (2)

• Resolvents for fractional-order operators with nonhomogeneous local boundary conditions
• Generation of semigroups for vector-valued pseudodifferential operators on the torus