Quantization for sequences of blow-up solutions to an elliptic equation having nonlocal exponential nonlinearity

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1. Verfasser: Gluck, Mathew
Format: Preprint
Veröffentlicht: 2025
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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