The concavity of Rényi entropy power for the parabolic p-Laplace equations and applications
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In this paper, we prove that the concavity of Rényi entropy power of positive solutions to the parabolic p-Laplace equations on compact Riemannian manifold with nonnegative Ricci curvature. As applications, we derive the improved \(L^p\)-Gagliardo-Nirenberg inequalities.
Mathematics Subject ClassificationPrimary 58J35 35K92 Secondary 35B40 35K55
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This work has been partially supported by the National Science Foundation of China, NSFC (Grant No. 11701347). The authors are thankful to the anonymous reviewers and editors for their constructive comments and suggestions on the earlier version for this paper.
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