Abstract
For Ω ⊂ ℝn and 2n/(n − 2) < p ⩽ (2n − 4)/(n − 4), we study the functional E 2 ( u ) = 1 2 ∫ Ω ( Δ u + | u | p − 2 u ) 2 d x . In an appropriate nonlinear space, the minimization problem can be solved using the direct method. We also construct solutions of the gradient flow.
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