论文标题
$ \ MATHCAL {A} $ - Quasiconvexity，Gårding的不平等和PDE中的应用程序中的应用程序和静态问题的限制性问题
$\mathcal{A}$-quasiconvexity, Gårding inequalities and applications in PDE constrained problems in dynamics and statics
论文作者
论文摘要
证明了与$ \ Mathcal {a} $ - Quasiconvex函数相关的二次形式的Gårding-type不平等。这种二次形式是保护定律理论中的相对熵，它与变异的计算中的Weierstrass多余功能有关。前者提供了弱的独特性结果，而后者已用于为局部最小化剂提供足够的定理。使用这种新的gårding不平等，我们将这些结果扩展到$ \ Mathcal {a} $ - Quasiconvexity假设下的Dynamics和静态问题的限制性问题。静态的应用程序通过证明经典$ \ Mathcal {a} = {\ rm curl} $ case中的$ l^p $本地最小值的唯一性来改善现有结果。
A Gårding-type inequality is proved for a quadratic form associated to $\mathcal{A}$-quasiconvex functions. This quadratic form appears as the relative entropy in the theory of conservation laws and it is related to the Weierstrass excess function in the calculus of variations. The former provides weak-strong uniqueness results, whereas the latter has been used to provide sufficiency theorems for local minimisers. Using this new Gårding inequality we provide an extension of these results to PDE constrained problems in dynamics and statics under $\mathcal{A}$-quasiconvexity assumptions. The application in statics improves existing results by proving uniqueness of $L^p$ local minimisers in the classical $\mathcal{A}= {\rm curl}$ case.
