外区域上的抛物型Monge—Ampère方程

代丽美

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 447-456.

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PDF(442 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 447-456. DOI: 10.12386/A2015sxxb0045
论文

外区域上的抛物型Monge—Ampère方程

    代丽美
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Parabolic Monge-Ampère Equations on Exterior Domains

    Li Mei DAI
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文章历史 +

摘要

研究外区域上的抛物型Monge—Ampère方程-utdet(D2u)=f解的存在性.利用Perron方法得到了该方程的外问题具有渐近性质解的存在性与唯一性.

Abstract

We study the existence of solutions to the parabolic Monge-Ampère equations-utdet(D2u)=f on the exterior domains. Using the Perron method, we get the existence and uniqueness of solutions with the asymptotic behavior to the exterior problems of parabolic Monge-Ampère equations.

关键词

抛物型Monge&mdash / Ampè / re方程 / 粘性解 / Perron方法 / 渐近性质

Key words

parabolic Monge-Ampère equations / viscosity solution / Perron method / asymptotic behavior

引用本文

导出引用
代丽美. 外区域上的抛物型Monge—Ampère方程. 数学学报, 2015, 58(3): 447-456 https://doi.org/10.12386/A2015sxxb0045
Li Mei DAI. Parabolic Monge-Ampère Equations on Exterior Domains. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 447-456 https://doi.org/10.12386/A2015sxxb0045

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基金

国家自然科学基金(11201343);山东省自然科学基金(ZR2011AL008);山东省优秀中青年科学家科研奖励基金(BS2011SF025)及省科技发展计划项目(2011YD16002)

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