On a dirichlet problem with a singular nonlinearity

Authors: Michael G. Crandall, Paul H. Rabinowitz, Luc Tartar - Communications in Partial Differential Equations 1977 cited by 706

Elliptic boundary value problems of the form Lu + g(x,u) in omega and u = 0 on the boundary of omega are studied where g is singular in that g(x,r) goes to infinity uniformly as r goes to zero from above. Existence of classical and generalized solutions is established and an associated nonlinear eigenvalue problem is treated. A detailed study is made of the behaviour of the solutions and their gradients near the boundary of omega. This leads to global estimates for the modulus of continuity of solutions. (Author)