Sobolev’s embedding on time scales

Author(s)

Naveed Ahmad, Institute of Business Administration, KarachiFollow
Hira Ashraf Baig, s, University of Swat, KPK
Ghaus ur Rahman, University of Swat, KPK
M. Shoaib Saleem, University of Okara

Author Affiliation

Naveed Ahmad is Assistant Professor of Mathematical Sciences at Institute of Business Administration (IBA), Karachi

Faculty / School

Faculty of Computer Sciences (FCS)

Department

Department of Mathematical Sciences

Was this content written or created while at IBA?

Yes

Document Type

Article

Source Publication

Journal of Inequalities and Applications

ISSN

1029-242X

Keywords

Embedding, Sobolev spaces, Time scales

Disciplines

Mathematics

Abstract

For 1 ≤ p< n, the embeddings of Sobolev spaces WΔ1,p(ΩTn) of functions defined on an open subset of an arbitrary time scale Tn, n≥ 1 , endowed with the Lebesgue Δ-measure have been developed in (Agarwal et al. in Adv. Differ. Equ. 2006:38121, 2006) for n= 1 and later generalized to arbitrary n≥ 1 in (Su et al. in Dyn. Partial Differ. Equ. 12(3):241–263, 2015). In this article we present the embeddings of Sobolev spaces WΔ1,p(ΩTn) for n≤ p≤ ∞ and then, using these embeddings, we develop general Sobolev’s embedding for the Sobolev spaces WΔ1,p(ΩTn) on time scales, where k is a non-negative integer and 1 ≤ p≤ ∞.

Indexing Information

HJRS - W Category, Scopus, Web of Science - Science Citation Index Expanded (SCI)

Journal Quality Ranking

Impact Factor: 2.491