Limiting Bourgain-Brezis estimates for systems of linear differential equations: Theme and variations

作者：Van Schaftingen Jean^*

来源：Journal of Fixed Point Theory and Applications, 2014, 15(2): 273-297.

DOI：10.1007/s11784-014-0177-0

• Critical Sobolev spaces
• Gagliardo-Nirenberg-Sobolev inequality
• canceling differential operator
• overdetermined elliptic systems
• underdetermined systems

J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case L (1) of singular integral estimates and the critical Sobolev space . This paper presents an overview of the results, further developments over the last ten years and challenging open problems.

• 出版日期2014-6