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• W1858609832 abstract "We consider the functional $$I_Omega(v) = int_Omega [f(|Dv|) - v] dx,$$ where $Omega$ is a bounded domain and $f$ is a convex function. Under general assumptions on $f$, G. Crasta [Cr1] has shown that if $I_Omega$ admits a minimizer in $W_0^{1,1}(Omega)$ depending only on the distance from the boundary of $Omega$, then $Omega$ must be a ball. With some restrictions on $f$, we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss how these results extend to more general settings, in particular to functionals that are not differentiable and to solutions of fully nonlinear elliptic and parabolic equations." @default.
• W1858609832 created "2016-06-24" @default.
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• W1858609832 date "2012-03-23" @default.
• W1858609832 modified "2023-10-06" @default.
• W1858609832 title "Symmetry of minimizers with a level surface parallel to the boundary" @default.
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• W1858609832 doi "https://doi.org/10.48550/arxiv.1203.5295" @default.
• W1858609832 hasPublicationYear "2012" @default.
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