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ALMOST EVERYWHERE R...
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Andersson, JohnKTH,Matematik (Inst.)
(author)
ALMOST EVERYWHERE REGULARITY FOR THE FREE BOUNDARY OF THE p-HARMONIC OBSTACLE PROBLEM p > 2
- Article/chapterEnglish2021
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2021-05-11
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American Mathematical Society (AMS),2021
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printrdacarrier
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LIBRIS-ID:oai:DiVA.org:kth-297821
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https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297821URI
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https://doi.org/10.1090/spmj/1654DOI
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Language:English
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Summary in:English
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Subject category:ref swepub-contenttype
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Subject category:art swepub-publicationtype
Notes
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QC 20210622
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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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KTHMatematik (Inst.)
(creator_code:org_t)
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In:St. Petersburg Mathematical Journal: American Mathematical Society (AMS)32:3, s. 415-4331061-00221547-7371
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