Various Properties of Solutions of the Infinity-Laplacian Equation
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Publication:5708016
DOI10.1080/03605300500258956zbMath1123.35018OpenAlexW1995499542MaRDI QIDQ5708016
Publication date: 25 November 2005
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605300500258956
Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Geometric theory, characteristics, transformations in context of PDEs (35A30)
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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
- On certain singular solutions of the partial differential equation \(u^ 2_ xu_{xx}+2u_ xu_ yu_{xy}+u^ 2_ yu_{yy}=0\)
- Some new PDE methods for weak KAM theory
- On the behaviour of \(\infty\)-harmonic functions near isolated points
- Extension of functions satisfying Lipschitz conditions
- On the partial differential equation \(u_ x^ 2 u_{xx} +2u_ x u_ y u_{xy} +u_ y^ 2 u_{yy} = 0\)
- A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions
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