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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
