Sobolev’s embedding on time scales
Faculty / School
Faculty of Computer Sciences (FCS)
Department of Mathematical Sciences
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Journal of Inequalities and Applications
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≤ ∞.
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Ahmad, N., Baig, H. A., Rahman, G. u., & Saleem, M. S. (2018). Sobolev’s embedding on time scales. Journal of Inequalities and Applications, 2018, 1-11. Retrieved from https://ir.iba.edu.pk/faculty-research-articles/172