On the optimal growth of functions with bounded Laplacian.
Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 2), are the objects of investigation in this paper. Using intrinsic scaling we establish the behavior of solutions near the free boundary. A consequence of this is that the time levels of the free boundary are porous (in N-dimension) and therefore its Hausdorff dimension is less than N. In particular the N-Lebesgue measure of the free boundary is zero for each t-level.
Let be either the unit ball or the half ball let be a strictly positive and continuous function, and let and solve the following overdetermined problem: where denotes the characteristic function of denotes the set and the equation is satisfied in the sense of distributions. When then we impose in addition that We show that a fairly mild thickness assumption on will ensure enough compactness on to give us...
Page 1