Variational inequalities (free boundaries), governed by the -parabolic equation (), 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 -dimension) and therefore its Hausdorff dimension is less than . In particular the -Lebesgue measure of the free boundary is zero for each -level.
Cite this article
Henrik Shahgholian, Analysis of the free boundary for the -parabolic variational problem . Rev. Mat. Iberoam. 19 (2003), no. 3, pp. 797–812DOI 10.4171/RMI/370