Quantization for sequences of blow-up solutions to an elliptic equation having nonlocal exponential nonlinearity
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918260390232064 |
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| author | Gluck, Mathew |
| author_facet | Gluck, Mathew |
| contents | This work provides a description of the asymptotic behavior of sequences of solutions to an elliptic equation with a nonlocal exponential nonlinearity of Choquard type. The equation under consideration is a nonlocal analog of the classical prescribed Gaussian curvature equation. A concentration-compactness alternative is established for sequences of solutions to the equation under consideration whenever suitable integrability assumptions on the solutions and the curvature functions are satisfied. Under further regularity assumptions on the curvature functions, and when blow-up occurs in the concentration-compactness alternative, an energy quantization result is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantization for sequences of blow-up solutions to an elliptic equation having nonlocal exponential nonlinearity Gluck, Mathew Analysis of PDEs 35J15 (Primary) 35J61, 35J91 (Secondary) This work provides a description of the asymptotic behavior of sequences of solutions to an elliptic equation with a nonlocal exponential nonlinearity of Choquard type. The equation under consideration is a nonlocal analog of the classical prescribed Gaussian curvature equation. A concentration-compactness alternative is established for sequences of solutions to the equation under consideration whenever suitable integrability assumptions on the solutions and the curvature functions are satisfied. Under further regularity assumptions on the curvature functions, and when blow-up occurs in the concentration-compactness alternative, an energy quantization result is established. |
| title | Quantization for sequences of blow-up solutions to an elliptic equation having nonlocal exponential nonlinearity |
| topic | Analysis of PDEs 35J15 (Primary) 35J61, 35J91 (Secondary) |
| url | https://arxiv.org/abs/2512.19865 |