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- W4376459504 abstract "<abstract><p>We obtain density estimates for the free boundaries of minimizers $ u ge 0 $ of the Alt-Phillips functional involving negative power potentials</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ int_Omega left(|nabla u|^2 + u^{-gamma} chi_{{u>0}}right) , dx, quad quad gamma in (0, 2). $end{document} </tex-math></disp-formula></p> <p>These estimates remain uniform as the parameter $ gamma to 2 $. As a consequence we establish the uniform convergence of the corresponding free boundaries to a minimal surface as $ gamma to 2 $. The results are based on the $ Gamma $-convergence of these energies (properly rescaled) to the Dirichlet-perimeter functional</p> <p><disp-formula> <label/> <tex-math id=FE2> begin{document}$ int_{Omega} |nabla u|^2 dx + Per_{Omega}({ u = 0}), $end{document} </tex-math></disp-formula></p> <p>considered by Athanasopoulous, Caffarelli, Kenig, and Salsa.</p></abstract>" @default.
- W4376459504 created "2023-05-14" @default.
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- W4376459504 date "2023-01-01" @default.
- W4376459504 modified "2023-09-29" @default.
- W4376459504 title "Uniform density estimates and $ Gamma $-convergence for the Alt-Phillips functional of negative powers" @default.
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- W4376459504 doi "https://doi.org/10.3934/mine.2023086" @default.
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