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Abstract We prove the concavity of p-Renyi entropy power for positive solutions to the doubly nonlinear diffusion equations on R n or compact Riemannian manifolds with nonnegative Ricci curvature. As… Click to show full abstract
Abstract We prove the concavity of p-Renyi entropy power for positive solutions to the doubly nonlinear diffusion equations on R n or compact Riemannian manifolds with nonnegative Ricci curvature. As applications, we give new proofs of the sharp L p -Sobolev inequality and L p -Gagliardo-Nirenberg inequalities on R n . Moreover, two improvements of L p -Gagliardo-Nirenberg inequalities are derived.
Keywords:
gagliardo nirenberg;
diffusion equations;
concavity;
doubly nonlinear;
nonlinear diffusion;
entropy power
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!