\(L^{\infty }\) variational problems for maps and the Aronsson PDE system

DOI10.1016/j.jde.2012.05.012zbMath1248.35074arXiv1105.4518OpenAlexW1846726811MaRDI QIDQ444927

Nikolaos I. Katzourakis

Publication date: 24 August 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.4518

zbMATH Keywords

absolute minimizersviscosity solutions\(\infty \)-Laplace systemAronsson PDE systemcalculus of variations in \(L^{\infty }\)vector-valued optimal Lipschitz extensions

Mathematics Subject Classification ID

Second-order elliptic systems (35J47) Existence theories in calculus of variations and optimal control (49J99) Quasilinear elliptic equations (35J62) Viscosity solutions to PDEs (35D40)

Related Items (24)

Weak vs. 𝒟-solutions to linear hyperbolic first-order systems with constant coefficients ⋮ ∞-minimal submanifolds ⋮ On the numerical approximation of \(\infty \)-harmonic mappings ⋮ On the Structure of ∞-Harmonic Maps ⋮ \(\mathcal{D}\)-solutions to the system of vectorial calculus of variations in \(L^\infty\) via the singular value problem ⋮ Second-order \(L^\infty\) variational problems and the \(\infty\)-polylaplacian ⋮ Explicit 2D \(\infty\)-harmonic maps whose interfaces have junctions and corners ⋮ Solutions of vectorial Hamilton-Jacobi equations are rank-one absolute minimisers in \(L^{\infty}\) ⋮ Rigidity and flatness of the image of certain classes of mappings having tangential Laplacian ⋮ Variational Problems in L^∞ Involving Semilinear Second Order Differential Operators ⋮ The convergence rate of p -harmonic to infinity-harmonic functions ⋮ Existence of $1D$ vectorial Absolute Minimisers in $L^\infty $ under minimal assumptions ⋮ A pointwise characterisation of the PDE system of vectorial calculus of variations in L^∞ ⋮ Existence and uniqueness of global strong solutions to fully nonlinear second order elliptic systems ⋮ Counterexamples in calculus of variations in \(L^{\infty}\) through the vectorial eikonal equation ⋮ Absolutely minimising generalised solutions to the equations of vectorial calculus of variations in \(L^\infty \) ⋮ Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems ⋮ Explicit \(\infty\)-harmonic functions in high dimensions ⋮ Vectorial variational principles in \(L^\infty\) and their characterisation through PDE systems ⋮ A New Characterisation of $\infty$-Harmonic and $p$-Harmonic Maps via Affine Variations in $L^\infty$ ⋮ Optimal ∞-Quasiconformal Immersions ⋮ Remarks on the validity on the maximum principle for the ∞-Laplacian ⋮ Nonuniqueness in vector-valued calculus of variations in \(L^\infty\) and some linear elliptic systems ⋮ The streamlines of ∞-harmonic functions obey the inverse mean curvature flow

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