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Tag: Sobolev space

  • Global regularity and blow-up criteria are established for a non-local equation

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    What the study found The study found that higher-order Sobolev solutions for a non-local integrable evolution equation can exist globally under a natural assumption on the initial momentum. It also identified a criterion for the existence of blow-up solutions. Why the authors say this matters The authors say the equation is related to pseudospherical surfaces…

  • Weighted Neumann eigenvalues are established for outward cuspidal domains

    Weighted Neumann eigenvalues are established for outward cuspidal domains

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    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…