Interior Schauder-type estimates for m − th order elliptic operators inrearrangement-invariant Sobolev spaces

Authors

EMİNAĞA M. MAMEDOVFollow
ŞEYMA ÇETİNFollow

Author ORCID Identifier

ŞEYMA ÇETİN: 0000-0003-2530-2470

EMİNAĞA MAMEDOV: 0009-0004-7873-0852

DOI

10.55730/1300-0098.3541

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.

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