Analytic solutions for the approximation of $p$-Laplacian problem

Xiaojun Lu; Xiaofen Lv

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arXiv · 1608.03052

Analytic solutions for the approximation of $p$-Laplacian problem

Xiaojun Lu·Xiaofen Lv

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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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Xiaojun Lu, Xiaofen Lv. 2016-08-10. Analytic solutions for the approximation of $p$-Laplacian problem. https://arxiv.org/abs/1608.03052

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