Normalized ground states for the critical Choquard equation with mixed fractional Laplacians

In this paper, we investigate the Schrödinger equation featuring mixed fractional Laplacians and critical exponent. By developing a generalized variant of Lieb’s translation theorem and employing a local minimization approach, we establish the existence of normalized solutions under appropriate conditions. Furthermore, we provide a detailed analysis of the regularity properties of these solutions, extending the understanding of such mixed-type operators in critical settings.