Geodesic
An obstacle-problem-like equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary
Georg S. Weiss1 orcid
1University of Tokyo, Japan
Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 121-128

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DOI

Concerning the obstacle-problem-like equation [Delta]u = [lambda]+/2 [chi]{u>0} [minus] [lambda][minus]/2 [chi]{u<0}, where [lambda]+ [ge] 0 and [lambda]+ + [lambda][minus] > 0, we prove regularity of the solution as well as an estimate on the Hausdorff dimension of the free boundary [Omega][cap] ([part]{u > 0} [cup] [part] {u < 0}). We apply this result to the Stefan-like equation [alpha][part]t max(v, 0) + [beta][part]t min(v, 0) [minus] [Delta]v = 0.
DOI : 10.4171/ifb/35
Classification : 46-XX, 60-XX
Mots-clés : Obstacle problem, two-phase problem, free boundary, monotonicity formula, frequency estimate, Hausdorff dimension

Georg S. Weiss  1

1 University of Tokyo, Japan 
Georg S. Weiss. An obstacle-problem-like equation with two phases: pointwise regularity of the solution and an estimate of the Hausdorff dimension of the free boundary. Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 121-128. doi: 10.4171/ifb/35
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     journal = {Interfaces and free boundaries},
     pages = {121--128},
     year = {2001},
     volume = {3},
     number = {2},
     doi = {10.4171/ifb/35},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/35/}
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