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 provide solvability for the Neumann spectral problem in this setting. They also indicate that the embeddings yield estimates for the weighted Neumann eigenvalues.
What the researchers tested
The researchers studied a nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. They used composition operators on Sobolev spaces to establish embeddings into weighted Lebesgue spaces.
What worked and what didn't
The Sobolev-space embeddings worked for the setting considered, and they supported solvability of the Neumann spectral problem. The abstract also states that the corresponding weighted Neumann eigenvalues can be estimated, but it does not give specific values or compare methods.
What to keep in mind
The abstract does not describe limitations, numerical examples, or conditions beyond the outward cuspidal domain setting with a weighted measure. No further scope restrictions are stated in the available summary.
Key points
- The paper studies a nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure.
- Composition operators on Sobolev spaces are used to establish embeddings into weighted Lebesgue spaces.
- The embeddings are said to give solvability of the Neumann spectral problem.
- The authors state that the corresponding weighted Neumann eigenvalues can be estimated.
- The abstract does not provide specific eigenvalue estimates or detailed limitations.
Disclosure
- Research title:
- Weighted Neumann eigenvalues are established for outward cuspidal domains
- Authors:
- Alexander Menovschikov, Alexander Ukhlov
- Institutions:
- National Research University Higher School of Economics, Ben-Gurion University of the Negev
- Publication date:
- 2026-04-21
- OpenAlex record:
- View
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