Pseudodifferential boundary value problems with non-smooth coefficients

Communications in Partial Differential Equations

Volumn 30, Issue 10, 2005, Pages 1463-1503

  Abels, Helmut ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Non smooth pseudodifferential operators; Pseudodifferential boundary value problems

Indexed keywords

EID: 27944478690     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605300500299554     Document Type: Article

References (26)

1. ∞-calculus. J. Math. Fluid. Mech. 7:223-260.
2. Abels, H. (2003). Stokes equations in asymptotically flat domains and the motion of a free surface. Ph.D. thesis, Technische Universität, Darmstadt. Aachen: Shaker Verlag.
3. Amann, H. (1997). Operator-valued fourier multipliers. Math. Nachr. 186:5-56.
4. Bergh, J., Löfström, J. (1976). Interpolation Spaces. Berlin-Heidelberg-New York: Springer.
5. Boutet de Monvel, L. (1971). Boundary problems for pseudo-differential operators. Acta Math. 126:11-51.
6. Edwards, R. E. (1965). Functional Analysis. New York, Chicago, San Francisco, Toronto, London: Holt, Rinehardt and Winston.
7. Fröhlich, A. (2001). Stokes- und Navier-Stokes-Gleichungen in Gewichteten Funktionenräumen. Ph.D. thesis, Teclinische Universität, Darmstadt. Aachen: Shaker Verlag.
8. Garcia-Cuerva, J., Rubio de Francia, J. L. (1985). Weighted Norm Inequalities and Related Topics. Amsterdam: North Holland.
9. Grubb, G. (1984). Singular green operators and their spectral asymptotics. Duke Math. 51:477-528.
10. p spaces. Comm. Part. Diff. Eq. 15:289-340.
11. p Sobolev spaces. Math. Z 218:43-90.
12. Grubb, G. (1996). Functional Calculus of Pseudodifferential Boundary Problems. 2nd ed. Basel, Boston, Berlin: Birkhäuser.
13. p-Sobolev spaces. J. Math. Fluid Mech. 3(1):57-81.
14. Grubb, G., Solonnikov, V. A. (1991). Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods. Math. Scand. 69:217-290.
15. p Sobolev spaces. Acta Math. 171:165-229.
16. Grubb, G., Schrohe, E. (2001). Trace expansions and the noncommutative residue for manifolds with boundary. J. Reine Angew. Math. 536:167-207.
17. Johnsen, J. (1996). Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Triebel-Lizorkin spaces. Math. Scand 79:25-85.
18. Kumano-Go, H. (1974). Pseudo-Differential Operators. Cambridge, Massachusetts, London: MIT Press.
19. Kumano-Go, H., Nagase, M. (1978). Pseudo-differential operators with non-regular symbols and applications. Funkcial Ekvac. 21:151-192.
20. p -estimates for pseudo-differential operators with nonregular symbols. Z Anal. Anwend. 10:493-501.
21. m. Comm. Part. Diff. Eq. 12(8):921-965.
22. Rempel, S., Schulze, B.-W. (1982). Index Theory of Elliptic Boundary Problems. Berlin: Akademie Verlag.
23. Schrohe, E. (2001). A short introduction to Boutet de Monvel's calculus. In: Gil, Juan et al., ed. Approaches to Singular Analysis. Based on workshop, Berlin, Germany, April 8-10, 1999. Oper. Theory, Adv. Appl. Vol. 125. Basel: Birkhäuser, pp. 85-116.
24. Stein, E. M. (1993). Harmonic Analysis. Princeton, New Jersey: Princeton Hall Press.
25. Taylor, M. E. (1991). Pseudodifferential Operators and Nonlinear PDE. Boston: Birkhäuser.
26. Triebel, H. (1978). Interpolation Theory, Function Spaces, Differential Operators. Amsterdam, New York, Oxford: North-Holland Publishing Company.