Abstract
We used a variational method based on optimal transport arguments to prove unique- ness of radial ground states for certain quasilinear elliptic equations, and we give the explicit expressions of the solutions. Our variational approach relies on a correspondence between the ground states of these equations and the equilibrium solutions of Fokker-Planck type equa- tions. Our method also allows to identify all the optimal functions of many geometric in- equalities, such as the Sobolev inequalities, the logarithmic Sobolev inequalities, and certain Gagliardo-Nirenberg inequalities.
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