\(C^1\)-regularity of the Aronsson equation in \(\mathbb{R}^2\)
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Publication:935267
DOI10.1016/j.anihpc.2007.03.003zbMath1179.35124OpenAlexW1992967834MaRDI QIDQ935267
Publication date: 6 August 2008
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/78805
Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)
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Cites Work
- \(C^1\) regularity for infinity harmonic functions in two dimensions
- Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
- An efficient derivation of the Aronsson equation
- \(L^\infty\) variational problems and Aronsson equations
- Minimization problems for the functional \(\displaystyle{\sup_x}\, F(x,f(x),f'(x))\). I, II
- Extension of functions satisfying Lipschitz conditions
- On the partial differential equation \(u_ x^ 2 u_{xx} +2u_ x u_ y u_{xy} +u_ y^ 2 u_{yy} = 0\)
- Minimization problems for functional supF(x, f(x), f'(x)). III
- Quasi-convexity and the lower semicontinuity of multiple integrals
- User’s guide to viscosity solutions of second order partial differential equations
- A tour of the theory of absolutely minimizing functions
- Generalized Cone Comparison Principle for Viscosity Solutions of the Aronsson Equation and Absolute Minimizers
- Minimizing theL∞Norm of the Gradient with an Energy Constraint
- The Euler equation and absolute minimizers of \(L^\infty\) functionals
- Lower semicontinuity of \(L^\infty\) functionals.
- Optimal Lipschitz extensions and the infinity Laplacian
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