论文标题
与混合线性 - 典型生长条件的拆卸类型的变分问题
Variational problems of splitting-type with mixed linear-superlinear growth conditions
论文作者
论文摘要
考虑使用混合线性 - 螺旋生长条件的拆卸类型的变异问题。在二维情况下，最小化问题由\ [j [w] = \int_Ω\ big [f_1 \ big（\ partial_1 w \ big） + f_2 \ big（\ partial_2 w \ big）\ big] \ big]合适的比较功能。在这里，$ f_1 $被认为是线性增长的凸能密度，$ f_2 $被认为是高等人的增长，例如由$ n $ unction提供，或者刚从下面的$ n $ function限制。这种问题的一种动机位于众所周知的超线性生长的分裂型问题与线性生长的分裂型问题（最近在[1]中）是与可塑性数学问题的联系（比较[2]）。在这里，我们证明了适当的放松方式的结果，包括近似程序，二元性，解决方案的存在和独特性以及一些新的更高的集成性结果。
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_Ω \Big[f_1\big(\partial_1 w\big) + f_2\big(\partial_2 w\big)\Big] \,dx \to \min \] w.r.t. a suitable class of comparison functions. Here $f_1$ is supposed to be a convex energy density with linear growth, $f_2$ is supposed to be of superlinear growth, for instance to be given by a $N$-function or just bounded from below by a $N$-function. One motivation for this kind of problem located between the well known splitting-type problems of superlinear growth and the splitting-type problems with linear growth (recently considered in [1]) is the link to mathematical problems in plasticity (compare [2]). Here we prove results on the appropriate way of relaxation including approximation procedures, duality, existence and uniqueness of solutions as well as some new higher integrability results.
