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arXiv · 2604.03752

On Coron problems with Choquard term and mixed operator

Jacques Giacomoni·Tuhina Mukherjee·Lovelesh Sharma
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Abstract

In this article, we study a Coron-type problem involving a critical Choquard nonlinearity driven by a mixed operator combining the Laplacian and fractional Laplacian. In annular-type domains, we prove the existence of nontrivial positive solutions when the inner hole is sufficiently small. Using variational methods and concentration compactness arguments, we establish a global compactness result for Palais- Smale sequences and obtain high-energy solutions using topological methods. We also derive regularity results for weak solutions.

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Jacques Giacomoni, Tuhina Mukherjee, Lovelesh Sharma. 2026-04-04. On Coron problems with Choquard term and mixed operator. https://arxiv.org/abs/2604.03752

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