Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).

Henrik Shahgholian

Revista Matemática Iberoamericana (2003)

  • Volume: 19, Issue: 3, page 797-812
  • ISSN: 0213-2230

Abstract

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Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p > 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.

How to cite

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Shahgholian, Henrik. "Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).." Revista Matemática Iberoamericana 19.3 (2003): 797-812. <http://eudml.org/doc/39643>.

@article{Shahgholian2003,
abstract = {Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p &gt; 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.},
author = {Shahgholian, Henrik},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones parabólicas; Problemas de frontera libre; Problemas variacionales; variational parabolic; nonlinear inequality; intrinsic scaling; regularity of free boundary},
language = {eng},
number = {3},
pages = {797-812},
title = {Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).},
url = {http://eudml.org/doc/39643},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Shahgholian, Henrik
TI - Analysis of the free boundary for the p-parabolic variational problem (p ≥ 2).
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 3
SP - 797
EP - 812
AB - Abstract Variational inequalities (free boundaries), governed by the p-parabolic equation (p &gt; 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.
LA - eng
KW - Ecuaciones parabólicas; Problemas de frontera libre; Problemas variacionales; variational parabolic; nonlinear inequality; intrinsic scaling; regularity of free boundary
UR - http://eudml.org/doc/39643
ER -

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