Hardy's inequality in a limiting case on general bounded domains

Jaeyoung Byeon, Futoshi Takahashi

In this paper, we study Hardy's inequality in a limiting case: $${\int }_{\Omega }|\nabla u{|}^{N}dx\ge C_N(\Omega ){\int }_{\Omega }\frac{|u(x){|}^N}{|x{|}^N{\left(\log \frac{R}{|x|}\right)}^N}dx$$ for func…