Existence of extremal functions in higher-order affine Sobolev inequalities

Key Points

• The aim is to demonstrate the existence of extremal functions within higher-order affine Sobolev inequalities.
• Utilized concentration-compactness methods
• Focused on spaces of integer regularity
• Applied techniques in spaces of fractional regularity
• Explored tools relevant for arbitrary regularity spaces
• Established existence of extremal functions for the inequalities
• Provided proofs potentially useful for other analytical contexts
• Demonstrated effectiveness of concentration-compactness methods in new scenarios