Analytic solutions for the approximation of $p$-Laplacian problem
Analytic solutions for the approximation of $p$-Laplacian problem
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发表时间：
2016-08
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通讯作者：
Xiaojun Lu;Xiaofen Lv
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作者：
Xiaojun Lu;Xiaofen Lv
本文主要研究p-Laplacian问题的近似解析解.通过一种近似机制，我们将具有Dirichlet边界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。
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.