Trudinger - Moser inequality on the whole plane with the exact growth condition
By S. Ibrahim, Nader Masmoudi, Kenji Nakanishi. 2011
80 citations recorded by the source corpus.
Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to $L^\infty$. It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modified versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function. It is tightly related to the ground state of the nonlinear Schrodinger equation (or the nonlinear Klein-Gordon equation), for which the range of the time phase (or the mass constant) as well as the energy is given by the best constant of the inequality.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/6faece66e8e69762d49546ac577385033258e7ea
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In Applied Mathematics
- Federica Sani
- Cristina Tarsi
- Nader Masmoudi
- Daniele Cassani
- G. Lu
- Nguyen Huong Lam
- Frédéric Rousset
- Peter Constantin
In Computational Theory and Mathematics
Citations in the corpus
- Equivalent Moser type inequalities in R2 and the zero mass case (2014, background): “proved in [37] the existence of extremal functions for the Adachi-Tanaka inequality in any dimensions. However, here we give a different proof, in fact our argument is an application of the results in [35] by Ibrahim, Masmoudi and Nakanishi concerning the two dimensional case. We point out that our a”
- Trudinger-Moser Inequalities with the Exact Growth Condition in ℝ N and Applications (2015, methodology): “In order to obtain this optimal descending growth condition, we argue as in [19] reducing the problem to a discrete version.”
- Adams' Inequality with the Exact Growth Condition in ℝ4 (2014, background): “R1/ > 1 following the longer arguments given in [21] and a proper use of Proposition 3.”