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• W1498717436 abstract "This paper is devoted to the Lin-Ni conjecture for a semi-linear elliptic equation with a super-linear, sub-critical nonlinearity and homogeneous Neumann boundary conditions. We establish a new rigidity result, that is, we prove that the unique positive solution is a constant if the parameter of the problem is below an explicit bound that we relate with an optimal constant for a Gagliardo-Nirenberg-Sobolev interpolation inequality and also with an optimal Keller-Lieb-Thirring inequality. Our results are valid in a sub-linear regime as well. The rigidity bound is obtained by nonlinear flow methods inspired by recent results on compact manifolds, which unify nonlinear elliptic techniques and the carr{e} du champ method in semi-group theory. Our method requires the convexity of the domain. It relies on integral quantities, takes into account spectral estimates and provides improved functional inequalities." @default.
• W1498717436 created "2016-06-24" @default.
• W1498717436 creator A5039729076 @default.
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• W1498717436 date "2014-12-09" @default.
• W1498717436 modified "2023-09-27" @default.
• W1498717436 title "Uniqueness and rigidity in nonlinear elliptic equations, interpolation inequalities and spectral estimates" @default.
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