Title

Sobolev’s embedding on time scales

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

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

Publication Status

Published

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