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- W2009366458 abstract "In this paper we study the behavior of the singular set $$ {u=|nabla u| =0}, $$for solutions u to the free boundary problem $$ Delta u = fchi_{{ugeq 0} } -gchi_{{u < 0}},$$with (f > 0), f(x) + g(x) 0, and c0 > 0 such that the density assumption $$ |{u < 0}cap B_r(z)|geq c_0r^2, qquad forall r < r_0,$$holds, then z is isolated. The density assumption can be motivated by the following example: $$ u=x_1^2, quad f=2, quad g < -2, quad hbox{and } {u < 0}=emptyset.$$" @default.
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- W2009366458 date "2007-01-09" @default.
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- W2009366458 title "The Singular Set for the Composite Membrane Problem" @default.
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- W2009366458 doi "https://doi.org/10.1007/s00220-006-0160-8" @default.
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