On the two-phase membrane problem with coefficients below the Lipschitz threshold
2009 (English)In: Annales de l'Institut Henri Poincare. Analyse non linéar, ISSN 0294-1449, Vol. 26, no 6, 2359-2372 p.Article in journal (Refereed) Published
We study the regularity of the two-phase membrane problem, with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C-1,C-1-regularity of the solution and that the free boundary is, near the so-called branching points, the union of two C-1-graphs. In our case, the same monotonicity formula does not apply in the same way. In the absence of a monotonicity formula, we use a specific scaling argument combined with the classification of certain global solutions to obtain C-1,C-1-estimates. Then we exploit some stability properties with respect to the coefficients to prove that the free boundary is the union of two Reifenberg vanishing sets near so-called branching points.
Place, publisher, year, edition, pages
2009. Vol. 26, no 6, 2359-2372 p.
FREE-BOUNDARY PROBLEMS; OBSTACLE-PROBLEM; DIFFERENTIAL EQUATIONS; 2 PHASES; REGULARITY
IdentifiersURN: urn:nbn:se:kth:diva-10334DOI: 10.1016/j.anihpc.2009.03.006ISI: 000272561600014ScopusID: 2-s2.0-71849090341OAI: oai:DiVA.org:kth-10334DiVA: diva2:214783