ALMOST EVERYWHERE REGULARITY FOR THE FREE BOUNDARY OF THE p-HARMONIC OBSTACLE PROBLEM p > 2

KTH Matematik (Inst) (creator_code:org_t)

2021-05-11
2021
Engelska.
Ingår i: St. Petersburg Mathematical Journal. - : American Mathematical Society (AMS). - 1061-0022 .- 1547-7371. ; 32:3, s. 415-433

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Abstract Ämnesord

Stäng

Let u be a solution to the normalized p-harmonic obstacle problem with p > 2. That is, u is an element of W-1,W-p(B-1(0)), 2 < p < infinity, u >= 0 and div(vertical bar del u vertical bar(p-2) del u) = chi({u>0}) in B-1(0) where u(x) >= 0 and chi(A) is the characteristic function of the set A. The main result is that for almost every free boundary point with respect to the (n - 1)-Hausdorff measure, there is a neighborhood where the free boundary is a C-1,C-beta-graph. That is, for Hn-1- a.e. point x(0) is an element of partial derivative{u > 0}boolean AND B-1(0) there is an r > 0 such that B-r(x(0))boolean AND partial derivative{u > 0} is an element of C-1,C-beta.

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