在无一致凸性条件下用奇异 Abreu 方程逼近带凸性约束的凸泛函极小元
偏微分方程分析
2020-02-12 v2
摘要
我们重新审视用 Abreu 型四阶方程解来逼近带凸性约束的某些凸泛函极小元的问题。该逼近问题在 Carlier-Radice（Approximation of variational problems with a convexity constraint by PDEs of Abreu type. Calc. Var. Partial Differential Equations. 58 (2019), no. 5, Art. 170）及作者本人（Singular Abreu equations and minimizers of convex functionals with a convexity constraint, arXiv:1811.02355v3, Comm. Pure Appl. Math., to appear）的先前工作中，于 Lagrangian 与约束障碍二者均一致凸的假设下被研究。通过引入一种新的逼近格式，我们完全去除了 Lagrangian 与约束障碍二者的一致凸性要求。我们的分析适用于受经济学中垄断者问题的原始二维 Rochet-Choné 模型启发的变分问题，以及弹性力学中漂浮弹性壳皱褶模式分析所产生的变分问题。
引用
@article{arxiv.1910.01486,
title = {On approximating minimizers of convex functionals with a convexity constraint by singular Abreu equations without uniform convexity},
author = {Nam Q. Le},
journal= {arXiv preprint arXiv:1910.01486},
year = {2020}
}
备注
v2: final version incorporating suggestions from the referee report; the derivations of (3.3) and (3.5) are included; to be published in Proc. Roy. Soc. Edinburgh Sect. A