Interior Schauder-type estimates for m - th order elliptic operators in rearrangement-invariant Sobolev spaces
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Tubitak scientific & technological research council Turkey
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this study, we investigate the m-th order elliptic operators on n-dimensional bounded domain ohm subset of R n with discontinuous coefficients in the rearrangement-invariant Sobolev space W X m (ohm). In general, the considered rearrangement-invariant spaces are not separable, so the use of classical methods in these spaces requires substantial modification of classical methods and a lot of preparation, concerning correctness of substitution operator, problems related to the extension operator in such spaces, etc. For this purpose, the corresponding separable subspaces of these spaces, in which the set of compact supported infinitely differentiable functions is dense, are introduced based on the shift operator. We establish interior Schauder-type estimates in the above subspaces. Note that Lebesgue spaces L p (ohm), grand-Lebesgue spaces, Marcinkiewicz spaces, weak-type L w p spaces, etc. are also covered by such spaces.
Açıklama
Anahtar Kelimeler
Banach Function Space, Rearrangement-Invariant Spaces, Sobolev Spaces, Elliptic Operator, Schauder Type Estimate
Kaynak
Turkish journal of mathematics
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
48
Sayı
4
Künye
MAMEDOV, E. M., & Çetin, Ş. (2024). Interior Schauder-type estimates for m− th order elliptic operators inrearrangement-invariant Sobolev spaces. Turkish Journal of Mathematics, 48(4), 793-816.
