Abstract
This paper is concerned with maximization and minimization problems related to a boundary value problem involving a p-Laplacian type operator. These optimization problems are formulated relative to the rearrangement of a fixed function. Firstly, by introducing a truncated function, we establish the existence and uniqueness of the solution of the boundary value problem involving a p-Laplacian type operator, and then, we show that both optimization problems are solvable under some suitable assumptions. Furthermore, we show that the solution of the minimization problem is unique and has some symmetric property if the domain considered is a ball.
Acknowledgments
The authors express their thanks very much for the valuable comments that are given by the referees.
Disclosure statement
No potential conflict of interest was reported by the author(s).