On the One-Dimensional Singular Abreu Equations

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....

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 90; no. 2; p. 35
Main Author Kim, Young Ho
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2024
Springer Nature B.V
Subjects
Approximation
Calculus of Variations and Optimal Control; Optimization
Control
Convexity
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Simulation
Systems Theory
Theoretical
Fourth-order equation
Singular Abreu equation
A priori estimate
Second boundary value problem
35J40
35B45
Characterization of minimizers
35B65
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ISSN0095-4616
1432-0606
DOI10.1007/s00245-024-10178-7

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Summary: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.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-024-10178-7