Revista Matemática Iberoamericana


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Volume 19, Issue 3, 2003, pp. 797–812
DOI: 10.4171/RMI/370

Published online: 2003-12-31

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

Henrik Shahgholian[1]

(1) KTH Royal Institute of Technology, Stockholm, Sweden

Variational inequalities (free boundaries), governed by the $p$-parabolic equation ($p\geq 2$), 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 $N$-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.

Keywords: Variational problem, inhomogeneous $p$-parabolic equation, free boundary, porosity

Shahgholian Henrik: Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$. Rev. Mat. Iberoam. 19 (2003), 797-812. doi: 10.4171/RMI/370