Weak local Gagliardo-Nirenberg type inequalities with a BMO term

An improvement of a global Gagliardo-Nienberg inequality with a BMO term is established.

💡 Research Summary

This paper presents a significant improvement and localization of Gagliardo-Nirenberg type inequalities that incorporate a Bounded Mean Oscillation (BMO) term. The primary motivation stems from the study of regularity for weak solutions to elliptic and parabolic partial differential equation (PDE) systems, where controlling the BMO norm of a solution is often a critical step towards establishing Hölder continuity or even global existence of classical solutions.

The authors’ first main objective is to extend previous global, “strong” inequalities (from cited works like