论文标题
在$ l^\ infty $中，与一般非线性限制的等等学矢量最小化问题
On isosupremic vectorial minimisation problems in $L^\infty$ with general nonlinear constraints
论文作者
论文摘要
我们研究了一般准甘维克斯一阶功能的$ l^\ infty $中的最小化问题，在该功能中，可允许的映射类别受到另一个至上功能的级别集合的限制，并由非线性操作员的零集。可允许的操作员的示例包括那些表达点，单方面，整体等级，椭圆形的准线性差异，Jacobian和Null Lagrangian约束的示例。通过$ l^p $近似为$ p \ to \ infty $的方法，我们说明存在特殊的$ l^\ infty $ minimiser，该$ l^\ minimiser求解了涉及某些辅助度量作为系数的Divergence PDE系统。该系统可以看作是Aronsson PDE系统的差异形式，该系统与受约束的$ l^\ infty $变分问题相关联。
We study minimisation problems in $L^\infty$ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Examples of admissible operators include those expressing pointwise, unilateral, integral isoperimetric, elliptic quasilinear differential, jacobian and null Lagrangian constraints. Via the method of $L^p$ approximations as $p\to \infty$, we illustrate the existence of a special $L^\infty$ minimiser which solves a divergence PDE system involving certain auxiliary measures as coefficients. This system can be seen as a divergence form counterpart of the Aronsson PDE system which is associated with the constrained $L^\infty$ variational problem.
