New Functional Inequalities with Applications to the Arctan-Fast Diffusion Equation
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DOI: 10.1007/s00009-025-02842-1
Abstract: In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads ∫S1arctan∂xuu∂xudx⩾arctanuW˙1,1(S1)uW˙1,1(S1).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}… read more here.
Keywords: arctan fast; diffusion equation; document; fast diffusion ... See more keywords