A minimization problem related to the principal frequency of the p -Bilaplacian with coupled Dirichlet–Neumann boundary conditions
Maria Fărcăşeanu, Mihai Mihăilescu, Denisa Stancu‐Dumitru · Electronic journal of qualitative theory of differential equations · 2023
For each fixed integer N ≥ 2 let Ω ⊂ R N be an open, bounded and convex set with smooth boundary. For each real number p ∈ ( 1 , ∞ ) define M ( p ; Ω ) = inf u ∈ W C 2 , ∞ ( Ω ) ∖ { 0 } ∫ Ω ( exp ( | Δ u | p ) − 1 ) d x ∫ Ω ( exp ( | u | p ) − 1 ) d x , where W C 2 , ∞ ( Ω ) := ∩ 1 < p < ∞ { u ∈ W 0