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Bibliographic Details
Main Author: Kim, Young Ho
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.07852
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author Kim, Young Ho
author_facet Kim, Young Ho
contents Singular fourth-order Abreu equations have been used to approximate minimizers of convex functionals subject to a convexity constraint in dimensions higher than or equal to two. For Abreu type equations, they often exhibit different solvability phenomena in dimension one and dimensions at least two. We prove the analogues of these results for the variational problem and singular Abreu equations in dimension one, and use the approximation scheme to obtain a characterization of limiting minimizers to the one-dimensional variational problem.
format Preprint
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institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the One-dimensional Singular Abreu Equations
Kim, Young Ho
Analysis of PDEs
Singular fourth-order Abreu equations have been used to approximate minimizers of convex functionals subject to a convexity constraint in dimensions higher than or equal to two. For Abreu type equations, they often exhibit different solvability phenomena in dimension one and dimensions at least two. We prove the analogues of these results for the variational problem and singular Abreu equations in dimension one, and use the approximation scheme to obtain a characterization of limiting minimizers to the one-dimensional variational problem.
title On the One-dimensional Singular Abreu Equations
topic Analysis of PDEs
url https://arxiv.org/abs/2403.07852