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Del Pino, Manuel; Dolbeault, Jean

Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. (English) Zbl 1112.35310

J. Math. Pures Appl. (9) 81, No. 9, 847-875 (2002).
Summary: In this paper, we find optimal constants for 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.

Cited in 3 Reviews
Cited in 194 Documents

MSC:

35J20 Variational methods for second-order elliptic equations
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49J40 Variational inequalities
35K57 Reaction-diffusion equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

Gagliardo-Nirenberg inequalities; Logarithmic Sobolev inequality; Optimal constants; Nonlinear diffusions; Entropy
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References:

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