Rellich inequalities with weights

By P. Caldiroli, R. Musina. 2011

74 citations recorded by the source corpus.

Let Ω be a cone in $${\mathbb {R}^{n}}$$ with n ≥  2. For every fixed $${\alpha \in \mathbb {R}}$$ we find the best constant in the Rellich inequality $${\int\nolimits_{\Omega}|x|^{\alpha}|\Delta u|^{2}dx \ge C\int\nolimits_{\Omega}|x|^{\alpha-4}|u|^{2}dx}$$ for $${u \in C^{2}_{c}(\overline\Omega\setminus\{0\})}$$ . We also estimate the best constant for the same inequality on $${C^{2}_{c}(\Omega)}$$ . Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/373a56157d6b64b57820ba7e0c1596d1c2ff0b1c

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In Applied Mathematics

1. D. Ganguly
2. Elvise Berchio
3. G. Grillo
4. Juan Luis V'azquez
5. Qiaohua Yang
6. Guozhen Lu
7. M. Porzio

In Computational Theory and Mathematics

1. G. Grillo
2. Juan Luis V'azquez
3. M. Porzio

Citations in the corpus

• Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, background): “without any claim for completeness [6, 12, 16, 22, 23, 33, 39].”