Multiple nonsmooth solutions for nonconvex variational boundary value problems in $\mathbb{R}^n$

Xiaojun Lu; David Yang Gao

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arXiv · 1607.05803

Multiple nonsmooth solutions for nonconvex variational boundary value problems in $\mathbb{R}^n$

Xiaojun Lu·David Yang Gao

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Abstract

This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or mixed boundary conditions can be converted into an algebraic equation, which can be solved analytically to obtain all solutions in the dual space. Both global and local extremality conditions are identified by the triality theory. In the application part, typical mechanical models with specificsources and boundary conditions in $\mathbb{R}^2$ are exhibited.

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BibTeX RIS

Xiaojun Lu, David Yang Gao. 2016-07-20. Multiple nonsmooth solutions for nonconvex variational boundary value problems in $\mathbb{R}^n$. https://arxiv.org/abs/1607.05803

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