Existence of extremals for stability of nonlocal Sobolev inequality

Key Points

• Optimal stability constants for the Sobolev inequality were explicitly determined, enhancing the understanding of its behavior.
• The single-bubble regime was rigorously analyzed to find the lowest stability constant, known as c_HLS, under variational methods.
• A mathematical framework was established for assessing the stability of the nonlocal Sobolev inequality, focusing on function behavior.
• This analysis provides insights into stability frameworks, though further exploration in multi-bubble scenarios may be required.