Sharp trace Gagliardo–Nirenberg–Sobolev inequalities for convex cones,and convex domains |
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| Authors: | Simon Zugmeyer |
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| Institution: | Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France |
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| Abstract: | We find a new sharp trace Gagliardo–Nirenberg–Sobolev inequality on convex cones, as well as a sharp weighted 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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| Keywords: | Sobolev inequality Gagliardo–Nirenberg–Sobolev inequality Hamilton–Jacobi equation |
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