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Existence and non-existence of extremal functions for inequalities of Bliss-Moser type
We establish a concentration--compactness theory for a one-dimensional singular Moser-type functional with logarithmic weight function $$\sup\limits_{v\in E }\int_0^1 e^{\left(\log\frac{e}{s}+γ\log\log\frac{e}{s}\right)\frac{v^2(s)}{s}}ds<\infty,~γ\in[0,1],$$ where $$E:= \left\{u \in H^{1}(0, 1): u(
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