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.File in questo prodotto:
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