On the Convergence of Solutions of Variational Problems with Implicit Pointwise Constraints in Variable Domains

Аннотация

Results on the convergence of minimizers and minimum values of integral and more general functionals J_s: W^1,p(Ω_s) → ℝ on the sets U_s(h_s) = {v ∈ W^1,p(Ω_s): h_s(v) ≤ 0 a.e. in Ω_s}, where p > 1, {Ω_s} is a sequence of domains contained in a bounded domain Ω of ℝⁿ (n > 2), and {h_s} is a sequence of functions on ℝ, are announced.