Turkish Journal of Mathematics
Abstract
In this study, we investigate the m-th order elliptic operators on n-dimensional bounded domain Ω ⊂ Rnwith discontinuous coefficients in the rearrangement-invariant Sobolev space WmX (Ω). In general, the consideredrearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantialmodification of classical methods and a lot of preparation, concerning correctness of substitution operator, problemsrelated to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of thesespaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on theshift operator. We establish interior Schauder-type estimates in the above subspaces. Note that Lebesgue spaces Lp (Ω),grand-Lebesgue spaces, Marcinkiewicz spaces, weak-type Lwpspaces, etc. are also covered by such spaces.
DOI
10.55730/1300-0098.3541
Keywords
Banach function space, elliptic operator, rearrangement-invariant spaces, Schauder type estimate, Sobolev spaces
First Page
793
Last Page
816
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
MAMEDOV, EMİNAĞA M. and ÇETİN, ŞEYMA
(2024)
"Interior Schauder-type estimates for m − th order elliptic operators inrearrangement-invariant Sobolev spaces,"
Turkish Journal of Mathematics: Vol. 48:
No.
4, Article 12.
https://doi.org/10.55730/1300-0098.3541
Available at:
https://journals.tubitak.gov.tr/math/vol48/iss4/12
