Analytic solutions for the approximation of p-Laplacian problem

2016/08/10 by Xiaojun Lu, Lu, Xiaojun, Xiaofen Lv +1
Computer Science · Engineering · Mathematics · #35J20 #35J60 #49K20 #80A20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #math.OC #msc:35J20 #msc:35J60 #msc:49K20 #msc:80A20

paper · pdf · doi:10.48550/arxiv.1608.03052

10 pages, 0 figure

arxiv created 2016/08/10 · openalex publication_date 2016/08/10 · arxiv updated 2016/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper mainly investigates the analytic solutions for the approximation of p-Laplacian problem. Through an approximation mechanism, we convert the nonlinear partial differential equation with Dirichlet boundary into a sequence of minimization problems. And a sequence of analytic minimizers can be obtained by applying the canonical duality theory. Moreover, the nonlinear canonical transformation gives a sequence of perfect dual maximization(minimization) problems, and further discussion shows the global extrema for both primal and dual problems.

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