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- W2964320629 abstract "We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality $${rm{sup}}left{ {left. {int_{rm{Omega }} {{rm{exp}}left( {alpha ;{rm{|}}u{{rm{|}}^{{N over {N - s}}}}} right)} } right|u in widetilde{W}_0^{s,p}({rm{Omega }}),;{{[u]}_{{W^{s,p}}({mathbb{R}^N})}} le 1} right} < infty $$ . Here Ω is a bounded domain of ℝN (N ≥ 2), s ∊ (0, 1), sp = N, $$widetilde{W}_0^{s,p}({rm{Omega }})$$ is a Sobolev-Slobodeckij space, and $${[ cdot ]_{{W^{s,p}}({mathbb{R}^N})}}$$ is the associated Gagliardo seminorm. We exhibit an explicit exponent α*s,N > 0, which does not depend on Ω, such that the Moser-Trudinger inequality does not hold true for α ∊ (α*s,N, +∞)." @default.
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- W2964320629 date "2019-07-01" @default.
- W2964320629 modified "2023-10-09" @default.
- W2964320629 title "On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces" @default.
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- W2964320629 doi "https://doi.org/10.1007/s11854-019-0029-3" @default.
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