Let Ω be a cone in R^n with n ≥ 2. For every fixed R we find the best constant in the Rellich inequality for u smooth and vanishing on ∂Ω. We also estimate the best constant for the same inequality for maps with compact support on Ω. Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains.

Rellich inequalities with weights

Musina, Roberta
2012-01-01

Abstract

Let Ω be a cone in R^n with n ≥ 2. For every fixed R we find the best constant in the Rellich inequality for u smooth and vanishing on ∂Ω. We also estimate the best constant for the same inequality for maps with compact support on Ω. Moreover we show improved Rellich inequalities with remainder terms involving logarithmic weights on cone-like domains.
2012
45
1-2
147
164
http://link.springer.com/article/10.1007/s00526-011-0454-3
Caldiroli, P; Musina, Roberta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32160
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