Scaling and variants of Hardy’s inequality
Abstract
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.
Publication Title
Proceedings of the American Mathematical Society
Recommended Citation
Goldstein, G., Goldstein, J., Mininni, R., & Romanelli, A. (2019). Scaling and variants of Hardy’s inequality. Proceedings of the American Mathematical Society, 147 (3), 1165-1172. https://doi.org/10.1090/proc/14295
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