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- W4386875487 abstract "We study a one-phase Bernoulli free boundary problem with weight function admitting a discontinuity along a smooth jump interface. In any dimension $Nge 2$, we show the $C^{1, alpha}$ regularity of the free boundary outside of a singular set of Hausdorff dimension at most $N-3$. In particular, we prove that the free boundaries are $C^{1, alpha}$ regular in dimension $N=2$, while in dimension $N=3$ the singular set can contain at most a finite number of points. We use this result to construct singular free boundaries in dimension $N=2$, which are minimizing for one-phase functionals with weight functions in $L^infty$ that are arbitrarily close to a positive constant." @default.
- W4386875487 created "2023-09-20" @default.
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- W4386875487 date "2023-09-17" @default.
- W4386875487 modified "2023-09-27" @default.
- W4386875487 title "Regularity for one-phase Bernoulli problems with discontinuous weights and applications" @default.
- W4386875487 doi "https://doi.org/10.48550/arxiv.2309.09283" @default.
- W4386875487 hasPublicationYear "2023" @default.
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