Elliptic problems in Besov and Sobolev—Triebel—Lizorkin spaces of low regularity
DOI:
https://doi.org/10.15407/dopovidi2021.06.003Keywords:
elliptic problem, Besov space, Sobolev space, Triebel–Lizorkin space, Fredholm operatorAbstract
Elliptic problems with additional unknown distributions in boundary conditions are investigated in Besov and Sobolev–Triebel–Lizorkin spaces of low regularity, specifically of an arbitrary negative order. We find that the problems induce Fredholm bounded operators on appropriate pairs of these spaces.
Downloads
References
Triebel, H. (1995). Interpolation theory, function spaces, differential operators [2nd ed.]. Heidelberg: Johann Ambrosius Barth.
Triebel, H. (1983). Theory of function spaces. Basel: Birkhäuser.
Magenes, E. (1965). Spazi di interpolazione ed equazioni a derivate parziali. In Atti del Settimo Congresso dell’Unione Matematica Italiana (Genoa, 1963) (pp. 134-197). Rome: Edizioni Cremonese.
Lions, J.-L. & Magenes, E. (1972). Non-homogeneous boundary-value problems and applications. Vol. I. Berlin, Heidelberg, New York: Springer.
Murach, A. A. (2009). Extension of some Lions–Magenes theorems. Methods Funct. Anal. Topology, 15, No. 2, pp. 152-167.
Mikhailets, V. A. & Murach, A. A. (2014). Hörmander spaces, interpolation, and elliptic problems. Berlin, Boston: De Gruyter.
Anop, A., Denk, R. & Murach, A. (2021). Elliptic problems with rough boundary data in generalized Sobolev spaces. Commun. Pure Appl. Anal., 20, No. 2, pp. 697-735. https://doi.org/10.3934/cpaa.2020286
Roitberg, Ya. (1996). Elliptic boundary value problems in the spaces of distributions. Dordrecht: Kluwer Acad. Publ.
Agranovich, M. S. (1997). Elliptic boundary problems. In Partial differential equations, IX. Encyclopaedia Math. Sci., Vol. 79 (pp. 1-144). Berlin: Springer.
Kozlov, V. A., Maz’ya, V. G. & Rossmann, J. (1997). Elliptic boundary value problems in domains with point singularities. Providence: American Math. Soc.
Johnsen, J. (1996). Elliptic boundary problems and the Boutet de Monvel calculus in Besov and Trie bel- Lizorkin spaces. Math. Scand., 79, No. 1, pp. 25-85. https://doi.org/10.7146/math.scand.a-12593
Grubb, G. (1990). Pseudo-differential boundary problems in spaces. Commun. Part. Diff. Eq., 15, No. 3, pp. 289-340. https://doi.org/10.1080/03605309908820688
Franke, J. & Runst, T. (1995). Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces. Math. Nachr., 174, pp. 113-149.
Hummel, F. (2021). Boundary value problems of elliptic and parabolic type with boundary data of ne gative regularity. J. Evol. Equ., 21, pp. 1945-2007. https://doi.org/10.1007/s00028-020-00664-0
Kalton, N., Mayboroda, S. & Mitrea, M. (2007). Interpolation of Hardy—Sobolev—Besov—Triebel—Li zor kin spaces and applications to problems in partial differential equations. In Interpolation theory and applications. Contemporary Mathematics, Vol. 445 (pp. 121-177). Providence, RI: American Math. Soc.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
