Frank, Rupert L. and Loss, Michael (2021) Existence of optimizers in a Sobolev inequality for vector fields. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211018-185216561
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Abstract
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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| 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 | ||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211018-185216561 | ||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 111517 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | George Porter | ||||||||
| Deposited On: | 19 Oct 2021 15:14 | ||||||||
| Last Modified: | 19 Oct 2021 15:14 |
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