Minimizing theL∞Norm of the Gradient with an Energy Constraint

DOI10.1080/03605300500299976zbMath1105.35028OpenAlexW1979063408MaRDI QIDQ5713477

R. Jensen, Emmanuel Nicholas Barron

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500299976

zbMATH Keywords

Lagrange multipliersEikonal equationelasto-plastic torsionAronsson-Euler equation

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational methods for second-order elliptic equations (35J20) Optimality conditions for free problems in two or more independent variables (49K10)

Related Items (14)

Generalised vectorial \(\infty\)-eigenvalue nonlinear problems for \(L^{\infty}\) functionals ⋮ The best constant and extremals of the Sobolev embeddings in domains with holes: the \(L^{\infty }\) case ⋮ Higher integrability of weak solutions to a class of double obstacle systems ⋮ \(L ^{\infty }\) variational problems with running costs and constraints ⋮ A minimisation problem in L^∞ with PDE and unilateral constraints ⋮ \(C^1\)-regularity of the Aronsson equation in \(\mathbb{R}^2\) ⋮ Nonsmooth convex functionals and feeble viscosity solutions of singular Euler-Lagrange equations ⋮ Structural analysis of an \(L\)-infinity variational problem and relations to distance functions ⋮ Uniqueness of ∞-Harmonic Functions and the Eikonal Equation ⋮ Derivation of the Aronsson equation for $C^1$ Hamiltonians ⋮ Uniqueness and nonuniqueness of viscosity solutions to Aronsson's equation ⋮ Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$ ⋮ Generalized Cone Comparison Principle for Viscosity Solutions of the Aronsson Equation and Absolute Minimizers ⋮ Vectorial variational problems in L ^∞ constrained by the Navier–Stokes equations*

Cites Work

• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• The \(\infty\)-eigenvalue problem
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• User’s guide to viscosity solutions of second order partial differential equations
• A tour of the theory of absolutely minimizing functions
• Direct methods in the calculus of variations
• The Euler equation and absolute minimizers of \(L^\infty\) functionals
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