Regularity of solutions of elliptic equations in divergence form in modified local generalized Morrey spaces
Yazarlar (4)
Prof. Dr. Vagıf GULIYEV
Baku State University, Azerbaycan
Baku State University, Azerbaycan
Rudn University, Rusya Federasyonu
Università Degli Studi Di Catania, İtalya
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Analysis and Mathematical Physics (Q1) | ||
| Dergi ISSN | 1664-2368 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | Türkçe | Basım Tarihi | 12-2020 |
| Cilt / Sayı / Sayfa | 11 / 1 / – | DOI | 10.1007/s13324-020-00433-9 |
| Makale Linki | http://dx.doi.org/10.1007/s13324-020-00433-9 | ||
| Özet |
| Aim of this paper is to prove regularity results, in some Modified Local Generalized Morrey Spaces, for the first derivatives of the solutions of a divergence elliptic second order equation of the form Lu:=∑i,j=1n(aij(x)uxi)xj=∇·f,for almost allx∈Ωwhere the coefficients aij belong to the Central (that is, Local) Sarason class CVMO and f is assumed to be in some Modified Local Generalized Morrey Spaces LM~{x0}p,φ. Heart of the paper is to use an explicit representation formula for the first derivatives of the solutions of the elliptic equation in divergence form, in terms of singular integral operators and commutators with Calderón–Zygmund kernels. Combining the representation formula with some Morrey-type estimates for each operator that appears in it, we derive several regularity results. |
| Anahtar Kelimeler |
| Elliptic equations | Integral operators | Morrey-type spaces | VMO |