$p$ -Laplacian问题的分析解
Analytic solutions for the approximation of $p$-Laplacian problem
摘要：
本文主要研究了$p$ -Laplacian问题的逼近的分析解。通过一种逼近机制，将带Dirichlet边值问题的非线性偏微分方程转化为一系列极小化问题。应用正则对偶理论，可以得到一个解析极小元序列。此外，非线性正则变换给出了一系列完美的对偶最大（最小）问题，并进一步讨论了原始和对偶问题的全局极值。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
