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 L_p-regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.
Maximal L_p-regularity of non-local boundary value problems
SEILER, Joerg
2015-01-01
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 L_p-regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.
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