论文标题
Monge-ampère类型的一类单数四阶方程的可溶性
Solvability of a class of singular fourth order equations of Monge-Ampère type
论文作者
论文摘要
我们研究了Monge-ampère类型的一类高度单数四阶方程的第二个边界值问题的可溶性。它们出现在使用ABREU类型方程的凸函数约束的近似值中。 Legendre变换和部分Legendre变换都用于我们的分析。在两个维度中，我们为高度单数ABREU方程式建立了全球解决方案，其中右侧的右侧为$ q $ -laplacian类型，用于所有$ q> 1 $。我们表明，在两个维度上具有凸限制的变异问题的最小化，这是由Rochet-Choné模型在垄断者的经济学问题中具有$ Q $ - 能力成本的经济学问题所产生的，可以通过Abreu方程的解决方案在统一的规范中近似于Abreu方程的解决方案。
We study the solvability of the second boundary value problem for a class of highly singular fourth order equations of Monge-Ampère type. They arise in the approximation of convex functionals subject to a convexity constraint using Abreu type equations. Both the Legendre transform and partial Legendre transform are used in our analysis. In two dimensions, we establish global solutions to the second boundary value problem for highly singular Abreu equations where the right hand sides are of $q$-Laplacian type for all $q>1$. We show that minimizers of variational problems with a convexity constraint in two dimensions that arise from the Rochet-Choné model in the monopolist's problem in economics with $q$-power cost can be approximated in the uniform norm by solutions of the Abreu equation for a full range of $q$.
