论文标题
扭曲的Harnack不平等和近似问题的近似，并通过单数Abreu方程构成凸的性约束
Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations
论文作者
论文摘要
我们在各个方面都表明，将变异问题与凸的限制最小化，这是由Rochet-choné模型产生的，在垄断者经济学问题中具有二次成本的Rochet-Choné模型可以通过单数Abreu方程的解决方案在统一的规范中近似。我们的abreu方程的难度包括只有在适当的子域中出现的奇异性，并且不能被任何转换完全消除。为了解决它们，我们依靠在这里建立的新工具：对于满足某些扭曲条件的奇异线性化蒙格 - 安am类型方程的harnack不平等。
We show in all dimensions that minimizers of variational problems with a convexity constraint, which arise from the Rochet-Choné model with a quadratic cost in the monopolist's problem in economics, can be approximated in the uniform norm by solutions of singular Abreu equations. The difficulty of our Abreu equations consists of having singularities that occur only in a proper subdomain and they cannot be completely removed by any transformations. To solve them, we rely on a new tool which we establish here: a Harnack inequality for singular linearized Monge-Ampère type equations that satisfy certain twisted conditions.
