On some variational problems set on domains tending to infinity

Abstract

Let Ω = ω 1 × ω 2 where ω 1 ⊂ R p and ω 2 ⊂ R n−p are assumed to be open and bounded. We consider the following minimization problem:E Ω (u ) = min u∈W 1,q 0 (Ω )

Study of fractional Poincaré inequalities on unbounded domains

“…Independently, various kinds of problems (mainly PDEs) on Ω have been considered, and their asymptotic behavior as → ∞ is studied. Such kind of theories are now well studied in the local case and for more details on this subject we refer [7], [8], [9], [17], [38] and the references therein.…”