Weighted Gagliardo-Nirenberg Inequalities Involving BMO Norms and Measures

TL;DR

This paper establishes weighted Gagliardo-Nirenberg inequalities involving BMO norms and measures, which are crucial for analyzing regularity and existence of solutions in complex degenerate or singular PDE systems.

Contribution

It introduces new weighted inequalities with doubling measures, advancing the tools available for studying strongly coupled parabolic and elliptic systems.

Findings

Proved global and local weighted Gagliardo-Nirenberg inequalities.

Applied inequalities to regularity theory of PDEs.

Facilitated existence proofs for solutions to degenerate or singular systems.

Abstract

Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and elliptic systems which are degenerate or singular because of the unboundedness of dependent and independent variables.