Scaling and variants of Hardy’s inequality
Gisèle Ruiz Goldstein, Jerome A. Goldstein, Rosa Maria Mininni, Silvia Romanelli · Proceedings of the American Mathematical Society · 2018
The two related one space dimensional singular linear parabolic equations (1), (2) studied by H. Brezis et al. [Comm. Pure Appl. Math. 24 (1971), pp. 395–416] have different scaling properties. These scaling properties lead to new variants of the Hardy and Caffarelli-Kohn-Nirenberg inequalities. These results are proved, and they imply some non-wellposedness results when the constant in the singular potential term is large enough.