Remarks on the Rellich inequality
The aim of the paper is to study the Rellich inequality \[ \Big\|\frac{f}{|x|^2}\Big\|_{L^2(\mathbb R^n)} \leq \frac{4}{n(n-4)} \, \|\Delta f\|_{L^2(\mathbb R^n)} \] for all \(f\) from the Sobolev space \(H^2(\mathbb R^n)\), with \(n \geq 5\). To prove this inequality, the authors make use of simple equalities involving partial derivatives and then they drop some convenient terms (remainders). Such an approach also shows the nonexistence of nontrivial extremisers of the Rellich inequality in question.
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