A minimisation problem in L∞ with PDE and unilateral constraints

DOI10.1051/cocv/2019034zbMath1451.35240arXiv1812.10093OpenAlexW2963995709MaRDI QIDQ5126403

Nikolaos I. Katzourakis

Publication date: 16 October 2020

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.10093

zbMATH Keywords

Lagrange multipliersRobin boundary conditionscalculus of variations in \(L^\infty \)PDE-constrained optimisationabsolute minimisersfluorescent optical tomographygeneralised Kuhn-Tucker theory

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Optimality conditions and duality in mathematical programming (90C46) Variational inequalities (49J40) Control/observation systems governed by partial differential equations (93C20) Biomedical imaging and signal processing (92C55) PDEs in connection with control and optimization (35Q93)

Related Items (4)

Generalised vectorial \(\infty\)-eigenvalue nonlinear problems for \(L^{\infty}\) functionals ⋮ A sufficient condition for the lower semicontinuity of nonlocal supremal functionals in the vectorial case ⋮ Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$ ⋮ Vectorial variational problems in L ^∞ constrained by the Navier–Stokes equations*

Cites Work

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• \(L ^{\infty }\) variational problems with running costs and constraints
• Uniqueness of absolute minimizers for \(L^\infty\)-functionals involving Hamiltonians \(H(x,p)\)
• Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains
• \(W^{1,p}\) estimates for elliptic problems with Neumann boundary conditions in Lipschitz domains
• On certain minimax problems and Pontryagin's maximum principle
• On the lower semicontinuity and approximation of \(L^\infty\)-functionals
• Elliptic equations in divergence form with partially BMO coefficients
• The eigenvalue problem for the \(\infty \)-Bilaplacian
• Existence, uniqueness and structure of second order absolute minimisers
• Uniform \(W^{1,p}\) estimates for an elliptic operator with Robin boundary condition in a \(\mathcal{C}^1\) domain
• Second-order \(L^\infty\) variational problems and the \(\infty\)-polylaplacian
• Minimization problems for the functional \(\displaystyle{\sup_x}\, F(x,f(x),f'(x))\). I, II
• Extension of functions satisfying Lipschitz conditions
• An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
• $\Gamma$-Convergence of Power-Law Functionals, Variational Principles in $L^{\infty},$ and Applications
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Optical tomography in medical imaging
• Robin boundary value problems on arbitrary domains
• Dielectric breakdown: optimal bounds
• Viscosity solutions of stationary Hamilton-Jacobi equations and minimizers of $L^{\infty }$ functionals
• A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian
• Existence of Minimizers for NonLevel Convex Supremal Functionals
• Homogenization of elliptic systems with Neumann boundary conditions
• Γ-convergence and absolute minimizers for supremal functionals
• Optical tomography as a PDE-constrained optimization problem
• Minimizing theL^∞Norm of the Gradient with an Energy Constraint
• Direct methods in the calculus of variations
• The Euler equation and absolute minimizers of \(L^\infty\) functionals

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