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Tag: Domain (mathematical analysis)

  • Minimal partitions can exist in unbounded domains

    Minimal partitions can exist in unbounded domains

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    What the study found The study finds that for unbounded domains, including domains of infinite volume, spectral minimal partitions can exist below a threshold determined by the essential spectrum and the best “k-1” partition energy. The behavior at the threshold differs by the choice of p: for p < ∞, minimizing partitions may or may…

  • Weighted Neumann eigenvalues are established for outward cuspidal domains

    Weighted Neumann eigenvalues are established for outward cuspidal domains

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    in

    What the study found The study establishes Sobolev-space embeddings into weighted Lebesgue spaces for a nonlinear Neumann eigenvalue problem in outward cuspidal domains. These embeddings are used to show solvability of the Neumann spectral problem and to estimate the associated weighted Neumann eigenvalues. Why the authors say this matters The authors say these embedding results…