Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domains
classification
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math.FA
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convexinequalitysharptraceconesgagliardo-nirenberg-sobolevaswellborell-brascamp-lieb
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We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality, coming from the Brunn-Minkowski theory.
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