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Existence of optimizers in a Sobolev inequality for vector fields

Frank, Rupert L. and Loss, Michael (2021) Existence of optimizers in a Sobolev inequality for vector fields. . (Unpublished)

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We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient in our proof is a version of the Rellich--Kondrachov compactness theorem for sequences satisfying a nonlinear constraint.

Item Type:Report or Paper (Discussion Paper)
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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2021 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Partial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and DMS-1856645 (M.L.) is acknowledged.
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Record Number:CaltechAUTHORS:20211018-185216561
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111517
Deposited By: George Porter
Deposited On:19 Oct 2021 15:14
Last Modified:19 Oct 2021 15:14

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