On the behaviour of the free boundary of some nonhomogeneous elliptic problems
Luis Álvarez · Applicable Analysis · 1990
The Nonlinear problem -△u+f(u) =g (x) in a domain Ω u=0 on ∂Ω is considered where we study the “non-diffusion” property (the support of u coincides with that of the function g(x)) under optimal conditions on g(x). Moreover we prove a pointwise "nondegeneracy" property (u grows faster than some function of the distance to the free boundary), and we give an application to the numerical approximation of the free boundary.