The limiting Dirac-Sobolev inequality

MSC:	35Q40	Equations from quantum mechanics
	35J50	Variational methods for elliptic systems
	46E35	Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Abstract:   We prove the critical Dirac-Sobolev inequality for p ∈ (1, 3). It follows that the Dirac Sobolev spaces are equivalent to classical Sobolev spaces if and only if p ∈ (1, 3). We prove the cocompactness of L^p* (R³ ) in H^1,p (R³ ). As an application, we prove the existence of minimizers to a class of isoperimetric problems.