Maximal $L_p$-regularity of non-local boundary value problems
Analysis of PDEs
2017-10-24 v1
Abstract
We investigate the -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 -bounded. Such operators appear as resolvents of non-local (pseudodifferential) boundary value problems. As a consequence, we obtain maximal -regularity for such boundary value problems. An example is given by the reduced Stokes equation in waveguides.
Cite
@article{arxiv.1407.2547,
title = {Maximal $L_p$-regularity of non-local boundary value problems},
author = {Robert Denk and Jörg Seiler},
journal= {arXiv preprint arXiv:1407.2547},
year = {2017}
}