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

2025/12/22 by M. Glück, Gluck, Mathew · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Advanced Mathematical Physics Problems

paper · doi:10.48550/arxiv.2512.19865

Abstract

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.

Citations

• An analysis of the two-vortex case in the Chern-Simons Higgs model
• On the equivalence of the first and second order equations for gauge theories

Cited by

• Complete Spectrum and Sharp Local Stability for the Critical Exponential Biharmonic Choquard Equation in \(\mathbb R⁴\)

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