In this paper, under several hypotheses and using a dual gap functional, weak sharp solutions are studied for a multidimensional variational-type inequality governed by \((\rho , \mathbf {b}, \mathbf {d})\)-convex multiple integral functional. Moreover, a relation between the minimum principle sufficiency property and weak sharpness of solutions for the considered multidimensional variational-type inequality is established.

中文翻译：

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与多维变分不等式相关的弱锐解

在本文中，在几个假设下并使用双间隙函数，研究了由\（（\ rho，\ mathbf {b}，\ mathbf {d}）\）-凸控制的多维变分型不等式的弱尖锐解。多重积分功能。此外，针对所考虑的多维变分型不等式，建立了最小原理充分性与弱弱解之间的关系。