Geodesic
Existence of optimizers in a Sobolev inequality for vector fields
Ars Inveniendi Analytica (2022).

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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.
Publié le :
DOI : 10.15781/rvnn-bp52 
@article{10_15781_rvnn_bp52,
     author = {Rupert L. Frank and Michael Loss},
     title = {Existence of optimizers in a {Sobolev} inequality for vector fields},
     journal = {Ars Inveniendi Analytica},
     publisher = {mathdoc},
     year = {2022},
     doi = {10.15781/rvnn-bp52},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.15781/rvnn-bp52/}
}
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Rupert L. Frank; Michael Loss. Existence of optimizers in a Sobolev inequality for vector fields. Ars Inveniendi Analytica (2022). doi : 10.15781/rvnn-bp52. http://geodesic.mathdoc.fr/articles/10.15781/rvnn-bp52/

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