Solvable optimization problems involving a p-Laplacian type operator. Issue 9 (13th June 2022)

• Record Type: Journal Article
• Authors: Qiu, Chong; Yang, Xiaoqi; Zhou, Yuying
• Is Part Of: Applicable analysis. Volume 101:Issue 9(2022)
• Page Start: 3246
• Page End: 3263
• Publication Date: 2022-06-13
• Subjects: Optimization -- rearrangement -- symmetric -- p-Laplacian; 35J20 -- 35J88 -- 49J40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1842372
• Languages: English
• ISSNs: 0003-6811

Abstract

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.