Multiple solutions of the planar $$L_p$$ dual Minkowski problem
Multiple solutions of the planar $$L_p$$ dual Minkowski problem
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DOI：
10.1007/s00526-021-01950-6
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发表时间：
2021-06
影响因子：
2.1
通讯作者：
Yongsheng Jiang;Zhengping Wang;Yonghong Wu
中科院分区：
文献类型：
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作者：
Yongsheng Jiang;Zhengping Wang;Yonghong Wu
研究了指数为p，q的平面Minkowski问题，通过对Sobolev空间中一个相关的约束变分问题的紧性分析，建立了平面对偶Minkowski问题的可解性及相关的泛函不等式，并在此基础上得到了平面对偶Minkowski问题的多重解.精确地说，如果是偶数，且至少存在对偶曲率度量等于平面上的标准球面度量的凸体，其中是的整数部分。
We are concerned with the planardual Minkowski problem with indicesp,q. Through the compactness analysis of an associated constrained variational problem in Sobolev space, the solvability of the planardual Minkowski problem and the related functional inequality are established, upon which the multiple solutions to the planardual Minkowski problem are obtained. Precisely, ifis even,and, there exist at leastconvex bodies whosedual curvature measure is equal to the standard spherical measure in the plane, whereis the integer part of.