Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces

ÇETİN, ŞEYMA; Zeren, Yusuf; Bilalov, Bilal; Sadigova, Sabina

doi:10.55730/1300-0098.3255

Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces

Bilal Bilalov, (Department of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan)

Yusuf ZEREN, (Yıldız Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Sabina Sadigova, (Laboratory of Mathematical Problems of Signal Processing, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan)

Şeyma ÇETİN (Yıldız Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)

Turkish Journal of Mathematics

9 0

Yıl: 2022 Cilt: 46 Sayı: 6 Sayfa Aralığı: 2078 - 2095 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3255 İndeks Tarihi: 09-12-2022

Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces

Öz:

In this work we consider the Sobolev spaces generated by the norm of the power weighted grand Lebesgue spaces. It is considered m –th order elliptic equation with nonsmooth coeﬀicients on bounded domain in $R^n$ . This space is nonseparable and by using shift operator we define the separable subspace of it, in which infinitely differentiable functions are dense. The investigation needs to establish boundedness property of convolution regarding weighted grand Lebesgue spaces. Then on scheme of nonweighted case we establish solvability (strong sense) in the small of m –th order elliptic equations in power weighted grand Sobolev spaces. Note that in weighted spaces this question is considered for the first time in connection with certain mathematical diﬀiculties.

Anahtar Kelime: Elliptic equation solvability in small weighted grand Lebesgue and Sobolev spaces

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	Bilalov B, Zeren Y, Sadigova S, ÇETİN Ş (2022). Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. , 2078 - 2095. 10.55730/1300-0098.3255
Chicago	Bilalov Bilal,Zeren Yusuf,Sadigova Sabina,ÇETİN ŞEYMA Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. (2022): 2078 - 2095. 10.55730/1300-0098.3255
MLA	Bilalov Bilal,Zeren Yusuf,Sadigova Sabina,ÇETİN ŞEYMA Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. , 2022, ss.2078 - 2095. 10.55730/1300-0098.3255
AMA	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. . 2022; 2078 - 2095. 10.55730/1300-0098.3255
Vancouver	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. . 2022; 2078 - 2095. 10.55730/1300-0098.3255
IEEE	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş "Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces." , ss.2078 - 2095, 2022. 10.55730/1300-0098.3255
ISNAD	Bilalov, Bilal vd. "Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces". (2022), 2078-2095. https://doi.org/10.55730/1300-0098.3255

APA	Bilalov B, Zeren Y, Sadigova S, ÇETİN Ş (2022). Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. Turkish Journal of Mathematics, 46(6), 2078 - 2095. 10.55730/1300-0098.3255
Chicago	Bilalov Bilal,Zeren Yusuf,Sadigova Sabina,ÇETİN ŞEYMA Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. Turkish Journal of Mathematics 46, no.6 (2022): 2078 - 2095. 10.55730/1300-0098.3255
MLA	Bilalov Bilal,Zeren Yusuf,Sadigova Sabina,ÇETİN ŞEYMA Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. Turkish Journal of Mathematics, vol.46, no.6, 2022, ss.2078 - 2095. 10.55730/1300-0098.3255
AMA	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. Turkish Journal of Mathematics. 2022; 46(6): 2078 - 2095. 10.55730/1300-0098.3255
Vancouver	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces. Turkish Journal of Mathematics. 2022; 46(6): 2078 - 2095. 10.55730/1300-0098.3255
IEEE	Bilalov B,Zeren Y,Sadigova S,ÇETİN Ş "Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces." Turkish Journal of Mathematics, 46, ss.2078 - 2095, 2022. 10.55730/1300-0098.3255
ISNAD	Bilalov, Bilal vd. "Solvability in the small of m–th order elliptic equations in weighted grand Sobolev spaces". Turkish Journal of Mathematics 46/6 (2022), 2078-2095. https://doi.org/10.55730/1300-0098.3255