Extremal functions for twisted sharp Sobolev inequalities with lower order remainder terms. The high-dimensional case

We prove existence of extremal functions and compactness of the set of extremal functions for twisted sharp 𝑛-dimensional Sobolev inequalities with lower order remainder terms when <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>5</m:mn> </m:mrow> </m:math> n≥ 5 .