Maximisation and minimisation on classes of rearrangements

DOI10.1017/S0308210500014840zbMath0736.49006OpenAlexW2054081733MaRDI QIDQ3984123

Geoffrey R. Burton, John Bryce McLeod

Publication date: 27 June 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500014840

zbMATH Keywords

rearrangementideal fluidnon-existence of minimiserstheory of steady vorticesweakly continuous convex functional

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonlinear boundary value problems for linear elliptic equations (35J65) Vortex flows for incompressible inviscid fluids (76B47)

Related Items (36)

Converse Symmetry and Intermediate Energy Values in Rearrangement Optimization Problems ⋮ Existence of steady multiple vortex patches to the vortex-wave system ⋮ Optimization problems for an elastic plate ⋮ Some optimization problems for \(p\)-Laplacian type equations ⋮ Stability of radially symmetric, monotone vorticities of 2D Euler equations ⋮ Extremal energies of Laplacian operator: different configurations for steady vortices ⋮ Rearrangement minimization problems with indefinite external forces ⋮ Cylindrical optimal rearrangement problem leading to a new type obstacle problem ⋮ A rearrangement minimization problem related to a nonlinear parametric boundary value problem ⋮ Local uniqueness of vortices for 2D steady Euler flow in a bounded domain ⋮ Tuning the total displacement of membranes ⋮ Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems ⋮ Nonlinear stability for stationary helical vortices ⋮ Variational problems on classes of rearrangements and multiple configurations for steady vortices ⋮ Design of a composite membrane with patches ⋮ On the stability of travelling waves with vorticity obtained by minimization ⋮ Bang-Bang and Multiple Valued Optimal Solutions of Control Problems Related to Quasi-linear Elliptic Equations ⋮ An iteration for steady vortices in rearrangement classes ⋮ A general existence theorem for a multi-valued control problem ⋮ Maximization of the first eigenvalue in problems involving the bi-Laplacian ⋮ Maximization and minimization in problems involving the bi-Laplacian ⋮ On 2D steady Euler flows with small vorticity near the boundary ⋮ Maximax and minimax rearrangement optimization problems ⋮ Linear convergence of a rearrangement method for the one-dimensional Poisson equation ⋮ Surface waves on steady perfect-fluid flows with vorticity ⋮ Nonlinear orbital stability for planar vortex patches ⋮ Optimal rearrangement problem and normalized obstacle problem in the fractional setting ⋮ Fractional optimal maximization problem and the unstable fractional obstacle problem ⋮ Extremal rearrangement problems involving Poisson's equation with Robin boundary conditions ⋮ Optimization of the First Eigenvalue of Equations with Indefinite Weights ⋮ Optimization problems on general classes of rearrangements ⋮ Global nonlinear stability for steady ideal fluid flow in bounded planar domains ⋮ Optimization of the first eigenvalue in problems involving the 𝑝-Laplacian ⋮ Monotonicity and stability of optimal solutions of a minimization problem ⋮ Numerical analysis of a free boundary problem with non-local obstacles ⋮ Constrained and unconstrained rearrangement minimization problems related to the \(p\)-Laplace operator

Cites Work

• Rearrangements of functions, maximization of convex functionals, and vortex rings
• Variational problems on classes of rearrangements and multiple configurations for steady vortices
• On Reachable Sets and Extremal Rearrangements of Control Functions

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