Second-order \(L^\infty\) variational problems and the \(\infty\)-polylaplacian

DOI10.1515/acv-2016-0052zbMath1437.49006arXiv1605.07880OpenAlexW2789940139MaRDI QIDQ2174609

Nikolaos I. Katzourakis, Tristan Pryer

Publication date: 21 April 2020

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.07880

zbMATH Keywords

Young measuresfully nonlinear equationsconvex integrationBaire category methodcalculus of variations in \(L^\infty\)generalised solutions\(\infty\)-bilaplacian\(\infty\)-polylaplacian

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical methods for partial differential equations, boundary value problems (65N99) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (14)

Structure and classification results for the ∞-elastica problem ⋮ Variational Problems in L^∞ Involving Semilinear Second Order Differential Operators ⋮ The \(\infty\)-elastica problem on a Riemannian manifold ⋮ Existence of $1D$ vectorial Absolute Minimisers in $L^\infty $ under minimal assumptions ⋮ Existence, uniqueness and structure of second order absolute minimisers ⋮ A minimisation problem in L^∞ with PDE and unilateral constraints ⋮ The r-Hunter–Saxton equation, smooth and singular solutions and their approximation ⋮ An $L^\infty$ Regularization Strategy to the Inverse Source Identification Problem for Elliptic Equations ⋮ A pointwise characterisation of the PDE system of vectorial calculus of variations in L^∞ ⋮ Generalised solutions for fully nonlinear PDE systems and existence-uniqueness theorems ⋮ Vectorial variational principles in \(L^\infty\) and their characterisation through PDE systems ⋮ Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$ ⋮ On the numerical approximation of p‐biharmonic and ∞‐biharmonic functions ⋮ A property of absolute minimizers in \(L^\infty\) calculus of variations and of solutions of the Aronsson-Euler equation

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