TY - JOUR

T1 - The inverse mean curvature flow as an obstacle problem

AU - Moser, Roger

PY - 2008

Y1 - 2008

N2 - The inverse mean curvature flow is a geometric evolution problem that is turned into a degenerate elliptic problem by a level set formulation. In the latter form, it may be regarded as a special case of an obstacle problem. In this paper, solutions of the problem are constructed with an approximation by p-harmonic functions and the use of appropriate barrier functions. This also extends the known existence results for weak solutions of the inverse mean curvature flow.

AB - The inverse mean curvature flow is a geometric evolution problem that is turned into a degenerate elliptic problem by a level set formulation. In the latter form, it may be regarded as a special case of an obstacle problem. In this paper, solutions of the problem are constructed with an approximation by p-harmonic functions and the use of appropriate barrier functions. This also extends the known existence results for weak solutions of the inverse mean curvature flow.

KW - p-harmonic

KW - inverse mean curvature flow

KW - obstacle problem

UR - http://www.scopus.com/inward/record.url?scp=57449113932&partnerID=8YFLogxK

UR - http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2008/57/3385

UR - http://dx.doi.org/10.1512/iumj.2008.57.3385

U2 - 10.1512/iumj.2008.57.3385

DO - 10.1512/iumj.2008.57.3385

M3 - Article

SN - 0022-2518

VL - 57

SP - 2235

EP - 2256

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 5

ER -