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Compactness via symmetrization |
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| Authors: | Almut Burchard Yan Guo |
| Affiliation: | a Department of Mathematics, University of Virginia, Charlottesville, VA 22902, USA b Division of Applied Mathematics, Brown University, Providence, RI 02912, USA |
| Abstract: | Consider two types of translation-invariant functionals  and  on  , and a sequence of functions fn whose corresponding symmetric rearrangements  are convergent. We show that fn themselves converge up to translations if either  or  . These compactness results lead to applications in variational problems and stability problems in stellar dynamics. |
| Keywords: | Symmetric rearrangement Concentration compactness Dynamical stability Hardy-Littlewood-Sobolev inequality Sobolev inequality Euler-Poisson system Vlasov-Poisson system Stellar dynamics |
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