Symmetry-breaking in a generalized Wirtinger inequality

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On a generalized Wirtinger inequality

Let α (p, q, r) = inf (ku0kp kukq : u ∈W 1,p per (−1, 1) \ {0} , Z 1 −1 |u|r−2 u = 0 ) . We show that α (p, q, r) = α (p, q, q) if q ≤ rp+ r − 1 α (p, q, r) < α (p, q, q) if q > (2r − 1) p generalizing results of Dacorogna-Gangbo-Subía and others. 1 The main result In the present article we discuss the following minimization problem α (p, q, r) = inf ( kukp kukq : u ∈W 1,p per (−1, 1) \ {0} , Z...

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ژورنال

عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations

سال: 2018

ISSN: 1292-8119,1262-3377

DOI: 10.1051/cocv/2017059