论文标题
能量弹药方程和差分夹杂物的通用不良性
Generic Ill-posedness of the Energy-Momentum Equations and Differential Inclusions
论文作者
论文摘要
我们表明，由Lagrangian满足通用对称条件的内部变化产生的能量摩孔方程是通常的。这是通过证明存在Lipschitz解决方案的子类也可以完成的，这些解决方案也是差分包含的解决方案。特别是这些解决方案可以是C1。我们证明，如果Lagrangian W是C1并且严格地排名一凸，这些解决方案不是固定点。鉴于Iwaniec，Kovalev和Onninen的Lipschitz规律性在尺寸2中求解了能量弹药方程，我们为不存在部分C1型的结果提供了足够的条件，即使在映射的条件下映射满足了正质雅各布的正面状态。最后，我们考虑了许多在非线性弹性和几何函数理论中研究的知名功能，并表明这些功能无法满足部分规律性的阻碍。
We show that the energy-momentum equations arising from inner variations whose Lagrangian satisfies a generic symmetry condition are generically ill-posed. This is done by proving that there exists a subclass of Lipschitz solutions that are also solutions to a differential inclusion. In particular these solutions can be nowhere C1. We prove that these solutions are not stationary points if the Lagrangian W is C1 and strictly rank-one convex. In view of the Lipschitz regularity result of Iwaniec, Kovalev and Onninen for solution of the energy-momentum equation in dimension 2 we give a sufficient condition for the non-existence of a partial C1-regularity result even under the condition that the mappings satisfy a positive Jacobian determinant condition. Finally we consider a number of well-known functionals studied in nonlinear elasticity and geometric function theory and show that these do not satisfy this obstruction to partial regularity.
