JournalsrmiVol. 19, No. 3pp. 797–812

Analysis of the free boundary for the pp-parabolic variational problem (p2)(p\ge 2)

  • Henrik Shahgholian

    KTH Royal Institute of Technology, Stockholm, Sweden
Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$ cover
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Abstract

Variational inequalities (free boundaries), governed by the pp-parabolic equation (p2p\geq 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 NN-dimension) and therefore its Hausdorff dimension is less than NN. In particular the NN-Lebesgue measure of the free boundary is zero for each tt-level.

Cite this article

Henrik Shahgholian, Analysis of the free boundary for the pp-parabolic variational problem (p2)(p\ge 2). Rev. Mat. Iberoam. 19 (2003), no. 3, pp. 797–812

DOI 10.4171/RMI/370