| Abstract: |
| This talk presents new sharp continuous and compact embeddings of nonlocal Sobolev spaces (of zero order) in Orlicz spaces and demonstrates the existence of a least-energy weak solution of the Brezis-Nirenberg type, logistic type problem and eigenvalue problem involving the logarithmic Laplacian. For the uniqueness of the solution, we present a new D\`iaz-Saa type inequality, which is of independent interest and can be applied to a larger class of problems. |
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