Existence of Faber-Krahn minimizers is established for compact Riemannian manifolds with a non-existence counterexample for non-compact cases, plus regularity up to a codimension-5 residual set via free-boundary methods.
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Flat free boundaries for the inhomogeneous one-phase Stefan problem are shown to be C^{1,α} via hodograph transform and linearization.
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Existence and regularity of Faber Krahn minimizers in a Riemannian manifold
Existence of Faber-Krahn minimizers is established for compact Riemannian manifolds with a non-existence counterexample for non-compact cases, plus regularity up to a codimension-5 residual set via free-boundary methods.
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Free boundary regularity for the inhomogeneous one-phase Stefan problem
Flat free boundaries for the inhomogeneous one-phase Stefan problem are shown to be C^{1,α} via hodograph transform and linearization.