Optimal control for cooperative systems involving fractional Laplace operators

Abstract

Abstract In this work, the elliptic 2 × 2 $2\times 2$ cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

Keywords

• 49J40
• 35R11
• 35J50
• 46E35