Weak Solutions of Nonlinear Elliptic Equations with Prescribed Singular Set

GivenΩany open and bounded subset of n,n 4, with smooth boundary and givenΣany (n−m)-dimensional compact submanifold ofΩwithout boundary,n>m>2, we prove the existence of weak solutions to the problem[formula]which are singular onΣ, whenpis a realp>m/(m−2), close to this value.