Nonuniqueness of solutions to the \(L_p\)-Minkowski problem

DOI10.1016/j.aim.2015.05.010zbMath1326.35009OpenAlexW652391911MaRDI QIDQ2354381

Jian Lu, Xu-Jia Wang, Huai-Yu Jian

Publication date: 13 July 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2015.05.010

zbMATH Keywords

Monge-Ampère equation

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Monge-Ampère equations (35J96)

Related Items (56)

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Cites Work

• The two dimensional \(L_p\) Minkowski problem and nonlinear equations with negative exponents
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
• Evolving plane curves by curvature in relative geometries
• Selfsimilar shrinking curves for anisotropic curvature flow equations
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• On the number of solutions to the discrete two-dimensional \(L_{0}\)-Minkowski problem.
• Motion of hypersurfaces by Gauss curvature
• Gauss curvature flow: The fate of the rolling stones
• On the regularity of solutions to a generalization of the Minkowski problem
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• Anisotropic flows for convex plane curves
• \(L_p\) Minkowski problem with not necessarily positive data
• Non-uniqueness of self-similar shrinking curves for an anisotropic curvature flow
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Deforming a hypersurface by its Gauss-Kronecker curvature
• Shapes of worn stones
• Classification of limiting shapes for isotropic curve flows
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Optimal Sobolev norms and the Lp Minkowski problem

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