## Revista Matemática Iberoamericana

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

Henrik Shahgholian

#### Abstract

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.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 19, Number 3 (2003), 797-812.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.rmi/1077293806

Mathematical Reviews number (MathSciNet)
MR2053564

Zentralblatt MATH identifier
1060.35065

#### Citation

Shahgholian, Henrik. Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$. Rev. Mat. Iberoamericana 19 (2003), no. 3, 797--812. https://projecteuclid.org/euclid.rmi/1077293806

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