高阶拟凸性约化为拟凸性
Higher order quasiconvexity reduces to quasiconvexity
摘要：
本文证明了适用于二阶导数问题变分处理的高阶拟凸函数可以作为经典拟凸函数推广到所有矩阵空间。精确地证明了在无穷远处具有p-增长的光滑严格2-拟凸函数（p>1）是具有相同增长的1-拟凸函数的对称矩阵的限制。作为结果，二阶变分问题的下半连续性结果被推导为著名的一阶定理的推论。
英文摘要：
In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it is proved that a smooth strictly 2-quasiconvex function with p-growth at infinity, p>1, is the restriction to symmetric matrices of a 1-quasiconvex function with the same growth. As a consequence, lower semicontinuity results for second-order variational problems are deduced as corollaries of well-known first order theorems.
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