On the generalized Hardy-Rellich inequalities
On the generalized Hardy-Rellich inequalities
Abstract In this paper, we look for the weight functions (say g ) that admit the following generalized Hardy-Rellich type inequality: $$\int_\Omega g (x)u^2 dx \les C\int_\Omega \vert \Delta u \vert ^2 dx,\quad \forall u\in {\rm {\cal D}}_0^{2,2} (\Omega ),$$ for some constant C > 0, where Ω is an …