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 -