Introduces Lebesgue W^{1,p}-extension domains and proves that any W^{1,p}-extension domain is Lebesgue for 1<p<∞, enabling reminiscent interpolation inequalities.
and Loss, Michael , TITLE =
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For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.
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Sobolev extensions, interpolation inequalities and consequences
Introduces Lebesgue W^{1,p}-extension domains and proves that any W^{1,p}-extension domain is Lebesgue for 1<p<∞, enabling reminiscent interpolation inequalities.
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A note on the Sobolev--Escobar bridge inequality
For T not equal to the Escobar threshold, the squared gradient norm minus Φ(T)^2 is bounded below by α_T times the squared distance to the minimizer set plus a higher-order term, for all functions in the constraint set A_T.