Revista Matemática Iberoamericana
- Rev. Mat. Iberoamericana
- Volume 19, Number 3 (2003), 797-812.
Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$
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.
Rev. Mat. Iberoamericana, Volume 19, Number 3 (2003), 797-812.
First available in Project Euclid: 20 February 2004
Permanent link to this document
Mathematical Reviews number (MathSciNet)
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
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