Hardy–Sobolev–Maz'ya type equations in bounded domains

We study the regularity, Palais–Smale characterization and existence/nonexistence of solutions of the Hardy–Sobolev–Maz'ya equation in a bounded domain in RN where x∈RN is denoted as x=(y,z)∈Rk×RN−k and . We show different behaviors of PS sequences depending on t=0 or t>0.