2000 character limit reached
Existence of optimizers in a Sobolev inequality for vector fields (2107.06450v2)
Published 14 Jul 2021 in math.AP, math-ph, math.CA, math.FA, and math.MP
Abstract: We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient in our proof is a version of the Rellich--Kondrachov compactness theorem for sequences satisfying a nonlinear constraint.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Collections
Sign up for free to add this paper to one or more collections.