Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
نویسندگان
چکیده
In this paper, we find optimal constants of a special class of Gagliardo-Nirenberg type inequalities which turns out to interpolate between the classical Sobolev inequality and the Gross logarithmic Sobolev inequality. These inequalities provide an optimal decay rate (measured by entropy methods) of the intermediate asymptotics of solutions to nonlinear diffusion equations.
منابع مشابه
Best Constants for Gagliardo-nirenberg Inequalities and Applications to Nonlinear Diiusions ?
In this paper, we nd optimal constants of a special class of Gagliardo-Nirenberg type inequalities which turns out to interpolate between the classical Sobolev inequality and the Gross logarithmic Sobolev inequality. These inequalities provide an optimal decay rate (measured by entropy methods) of the intermediate asymptotics of solutions to nonlinear diiusion equations.
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