Revista Matemática Iberoamericana

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

Henrik Shahgholian

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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.

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

First available in Project Euclid: 20 February 2004

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Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations 35K85: Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40] 35K65: Degenerate parabolic equations 35R35: Free boundary problems

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. Iberoamericana 19 (2003), no. 3, 797--812.

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