Inequalities for Green's operator applied to the minimizers

Abstract

Abstract In this paper, we prove both the local and global Lφ -norm inequalities for Green's operator applied to minimizers for functionals defined on differential forms in Lφ -averaging domains. Our results are extensions of Lp norm inequalities for Green's operator and can be used to estimate the norms of other operators applied to differential forms. 2000 Mathematics Subject Classification: Primary: 35J60; Secondary 31B05, 58A10, 46E35.

Keywords

• Green's operator
• minimizers
• inequalities and differential forms