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Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem. (English) Zbl 1175.35154

The authors construct two one-parameter families of monotonicity formulae for the study of free boundary points in a lower dimensional obstacle problem. They show the uniqueness and continuous dependence of the blowups at singular points of given homogeneity and prove a structural theorem for the singular set.

MSC:

35R35 Free boundary problems for PDEs
35B44 Blow-up in context of PDEs
35B33 Critical exponents in context of PDEs
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