Neumann problem for a quasilinear elliptic equation in a varying domain
Mamadou Sango · Comptes Rendus Mathématique · 2006
We investigate the Neumann problem for a nonlinear elliptic operator of Leray–Lions type in Ω ( s ) = Ω \ F ( s ) , s = 1 , 2 , … , where Ω is a domain in R n ( n ⩾ 3 ) , F ( s ) is a closed set located in the neighborhood of a ( n − 1 ) -dimensional manifold Γ lying inside Ω . We study the asymptotic behavior of u ( s ) as s → ∞ , when the set F ( s ) tends to Γ .