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December, 2003 Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$
Henrik Shahgholian
Rev. Mat. Iberoamericana 19(3): 797-812 (December, 2003).


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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Henrik Shahgholian. "Analysis of the free boundary for the $p$-parabolic variational problem $(p\ge 2)$." Rev. Mat. Iberoamericana 19 (3) 797 - 812, December, 2003.


Published: December, 2003
First available in Project Euclid: 20 February 2004

zbMATH: 1060.35065
MathSciNet: MR2053564

Primary: 35K55 , 35K65 , 35K85 , 35R35

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

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 3 • December, 2003
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