Partial differential equations of elliptic type in nonsmooth domains

This paper studies the problem -Delta u + lambda u = u(p) in nonsmooth domains with mixed boundary conditions. Special attention will be given here to the critical case and to domains which have no further regularity than a Lipschitzian boundary. For such domains, we obtain a generalized version of Cherrier's inequality and prove an existence result. This was achieved by using an extended definition of the manifold.