Study of complete abstract elliptic differential equations in non-commutative cases

Abstract

This article is devoted to abstract second-order complete elliptic differential equations set on the whole line in a non-commutative framework. Existence, uniqueness and maximal regularity of the strict solution are proved. This study is performed in BUC ^θ(ℝ; X).

Keywords:

• second-order abstract elliptic differential equations
• non-commutative case
• analytic semigroup
• maximal regularity

AMS Subject Classifications::

• 35J15
• 47D06
• 35B65

Acknowledgements

The authors would like to thank the referees for their very useful comments and remarks.