@article{bb6b89602d7d484391a38660e7fbfd11,
title = "Uniqueness of entire ground states for the fractional plasma problem",
abstract = " We establish uniqueness of vanishing radially decreasing entire solutions, which we call ground states, to some semilinear fractional elliptic equations. In particular, we treat the fractional plasma equation and the supercritical power nonlinearity. As an application, we deduce uniqueness of radial steady states for nonlocal aggregation-diffusion equations of Keller-Segel type, even in the regime that is dominated by aggregation. ",
keywords = "math.AP, 35K55, 35R11, 49K20",
author = "Hardy Chan and Gonz{\'a}lez, {Mar{\'i}a del Mar} and Yanghong Huang and Edoardo Mainini and Bruno Volzone",
note = "Funding Information: The authors wish to warmly thank Y. Sire, X. Cabr{\'e}, J. Dolbeault, N. Ikoma and L. Montoro for the fruitful discussions and valuable suggestions. This work has been partially supported by GNAMPA of the Italian INdAM (National Institute of High Mathematics). H.C. has received funding from the European Research Council under the Grant Agreement No 721675. M.d.M. Gonz{\'a}lez is supported by the Spanish government grant MTM2017-85757-P. E.M. acknowledges support from the MIUR-PRIN project No 2017TEXA3H and from the INdAM-GNAMPA 2019 project “Trasporto ottimo per dinamiche con interazione”. B.V. acknowledges support from the {\textquoteleft}Programma triennale della Ricerca dell{\textquoteright}Universit{\`a} degli Studi di Napoli “Parthenope” - Sostegno alla ricerca individuale 2015-2017” and the INDAM-GNAMPA 2019 project “Trasporto ottimo per dinamiche con interazione”. Funding Information: The authors wish to warmly thank Y. Sire, X. Cabr?, J. Dolbeault, N. Ikoma and L. Montoro for the fruitful discussions and valuable suggestions. This work has been partially supported by GNAMPA of the Italian INdAM (National Institute of High Mathematics). H.C. has received funding from the European Research Council under the Grant Agreement No 721675. M.d.M. Gonz?lez is supported by the Spanish government grant MTM2017-85757-P. E.M. acknowledges support from the MIUR-PRIN project No 2017TEXA3H and from the INdAM-GNAMPA 2019 project ?Trasporto ottimo per dinamiche con interazione?. B.V. acknowledges support from the ?Programma triennale della Ricerca dell?Universit? degli Studi di Napoli ?Parthenope? - Sostegno alla ricerca individuale 2015-2017? and the INDAM-GNAMPA 2019 project ?Trasporto ottimo per dinamiche con interazione?. Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = oct,
day = "26",
doi = "10.1007/s00526-020-01845-y",
language = "English",
volume = "59",
journal = "Calculus of Variations and Partial Differential Equations",
publisher = "Springer Nature",
number = "195",
}