On the Yamabe equation with rough potentials

Francesca Prinari, Nicola Visciglia

We study the existence of non--trivial solutions to the Yamabe equation: $$-\Delta u+a(x)=\mu u|u{|}^{\frac{4}{n-2}}\mu >0,x\in \Omega \subset {\mathbf{R}}^{n}withn\ge 4,$$ $$ u(x)=0 \h…