zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The structure of the free boundary for lower dimensional obstacle problems. (English) Zbl 1185.35339

Consider the obstacle problem consisting in looking for the minimizer u(x) of the Dirichlet integral over the unit ball B 1 in n (n3) among the elements of the closed convex set

K={vH 1 (B 1 ),v=ϕonB 1 ,v| x n =0 0}

where ϕ is a smooth function which is supposed to be positive on B 1 , intersected with x n =0 and to assume also negative values. The coincidence set λ(u) is the subset of x n =0 where u vanishes and we are also interested in the free boundary F(u), which is the boundary of the set {uφ}{x n =0}. The paper is concerned with the study of F(u), which is shown to be a C 1,α (n-2)-dimensional surface in n-1 near non-degenerate points.

35R35Free boundary problems for PDE
35J20Second order elliptic equations, variational methods