A New Characterisation of $\infty$-Harmonic and $p$-Harmonic Maps via Affine Variations in $L^\infty$
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Publication:2958564
zbMath1357.35088arXiv1509.01811MaRDI QIDQ2958564
Publication date: 3 February 2017
Full work available at URL: https://arxiv.org/abs/1509.01811
Young measures\(p\)-Laplacianfully nonlinear systems\(\infty\)-Laplaciangeneralised solutionscalculus of variations in \(L\)-\(\infty\)
Variational methods applied to PDEs (35A15) Degenerate elliptic equations (35J70) Second-order elliptic systems (35J47) Viscosity solutions to PDEs (35D40) Quasilinear elliptic equations with (p)-Laplacian (35J92)
Related Items (13)
Weak vs. 𝒟-solutions to linear hyperbolic first-order systems with constant coefficients ⋮ On the numerical approximation of \(\infty \)-harmonic mappings ⋮ \(\mathcal{D}\)-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 ⋮ 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 ⋮ 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∞ ⋮ 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 ⋮ The streamlines of ∞-harmonic functions obey the inverse mean curvature flow
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- Remarks on the validity on the maximum principle for the ∞-Laplacian
- Optimal ∞-Quasiconformal Immersions
- The Euler equation and absolute minimizers of \(L^\infty\) functionals
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