Maximal Lp-regularity of non-local boundary value problems
R. Denk and J. Seiler
Abstract. We investigate the 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 R-bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems. As a consequence, we obtain maximal Lp-regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.
Monatsh. Math. 176 (2015), 53-80.
Springer Link: doi:10.1007/s00605-014-0669-4
The paper is available here (preprint version).