Maximal $$L_{p}$$ L p -regularity of non-local boundary value problems
Copyright policy )Maximal $$L_{p}$$ L p -regularity of non-local boundary value problems
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.
- University of Turin Italy
- University of Konstanz Germany
boundary value problems, R-boundedness; maximal regularity; Waveguides; pseudodifferential operators; Boundary value problems, maximal regularity, R-boundedness, waveguide, 35S15, 35K50, Boundary value problems for PDEs with pseudodifferential operators, Geometry and structure of normed linear spaces, Mathematics - Analysis of PDEs, info:eu-repo/classification/msc/35S15, 35K50, Boutet de Monvel calculus, \(\mathcal{R}\)-boundedness, Initial-boundary value problems for higher-order parabolic equations, maximal Lp-regularity, Pseudodifferential operators, pseudodifferential operators, info:eu-repo/classification/ddc/510
boundary value problems, R-boundedness; maximal regularity; Waveguides; pseudodifferential operators; Boundary value problems, maximal regularity, R-boundedness, waveguide, 35S15, 35K50, Boundary value problems for PDEs with pseudodifferential operators, Geometry and structure of normed linear spaces, Mathematics - Analysis of PDEs, info:eu-repo/classification/msc/35S15, 35K50, Boutet de Monvel calculus, \(\mathcal{R}\)-boundedness, Initial-boundary value problems for higher-order parabolic equations, maximal Lp-regularity, Pseudodifferential operators, pseudodifferential operators, info:eu-repo/classification/ddc/510
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