Refined Convex Sobolev Inequalities

  title={Refined Convex Sobolev Inequalities},
  author={Anton Arnold and Jean Dolbeault},
This paper is devoted to refinements of convex Sobolev inequalities in the case of power law relative entropies: a nonlinear entropy–entropy production relation improves the known inequalities of this type. The corresponding generalized Poincaré type inequalities with weights are derived. Best constants are compared to the usual Poincaré constant. 
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