A PDE Perspective of the Normalized Infinity Laplacian
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Publication:3603835
DOI10.1080/03605300802289253zbMath1157.35388OpenAlexW2101445184MaRDI QIDQ3603835
Publication date: 19 February 2009
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/03605300802289253
well-posednessstability of solutionsviscosity solutionstug-of-war gameinhomogeneous equationcomparison propertynormalized infinity Laplacian
Related Items (46)
Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation ⋮ The eigenvalue problem for a class of degenerate operators related to the normalized \(p\)-Laplacian ⋮ Viscosity solutions to inhomogeneous Aronsson's equations involving Hamiltonians \(\langle A(x)p,p\rangle \) ⋮ Parabolic biased infinity Laplacian equation related to the biased tug-of-war ⋮ Characterization of stadium-like domains via boundary value problems for the infinity Laplacian ⋮ The sublinear problem for the 1-homogeneous 𝑝-Laplacian ⋮ An inhomogeneous evolution equation involving the normalized infinity Laplacian with a transport term ⋮ Power- and log-concavity of viscosity solutions to some elliptic Dirichlet problems ⋮ Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian ⋮ On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian ⋮ The Gelfand problem for the 1-homogeneous \(p\)-Laplacian ⋮ BOUNDARY BLOW-UP SOLUTIONS TO EQUATIONS INVOLVING THE INFINITY LAPLACIAN ⋮ Liouville Theorems for infinity Laplacian with gradient and KPP type equation ⋮ Global regularity for a class of fully nonlinear PDEs with unbalanced variable degeneracy ⋮ Boundary behavior of large solutions to the infinity Laplace equations on the half-line ⋮ Infinity-Laplacian type equations and their associated Dirichlet problems ⋮ Asymptotic boundary estimates to infinity Laplace equations with \(\Gamma\)-varying nonlinearity ⋮ The second order expansion of boundary blow-up solutions for infinity-Laplacian equations ⋮ A weighted eigenvalue problem of the degenerate operator associated with infinity Laplacian ⋮ Geometric gradient estimates for fully nonlinear models with non-homogeneous degeneracy and applications ⋮ Solutions to an inhomogeneous equation involving infinity Laplacian ⋮ Unnamed Item ⋮ Asymptotic estimates of boundary blow-up solutions to the infinity Laplace equations ⋮ The tug-of-war without noise and the infinity Laplacian in a wedge ⋮ On the best Lipschitz extension problem for a discrete distance and the discrete \(\infty \)-Laplacian ⋮ Solutions of nonlinear PDEs in the sense of averages ⋮ Blow-up rates of large solutions for infinity Laplace equations ⋮ The exact asymptotic behavior of boundary blow-up solutions to infinity Laplacian equations ⋮ Solutions to an inhomogeneous equation involving Aronsson operator ⋮ Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian ⋮ Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones ⋮ A boundary-value problem for normalized Finsler infinity-Laplacian equations with singular nonhomogeneous terms ⋮ Comparison principles for infinity-Laplace equations in Finsler metrics ⋮ Solutions for equations involving the infinity-Laplacian ⋮ A $C^1$ regularity result for the inhomogeneous normalized infinity Laplacian ⋮ Boundary behavior for the solutions to Dirichlet problems involving the infinity-Laplacian ⋮ Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian ⋮ A uniqueness result for the quasiconvex operator and first order PDEs for convex envelopes ⋮ On solutions to Dirichlet problems involving the infinity-Laplacian ⋮ A finite difference approach to the infinity Laplace equation and tug-of-war games ⋮ A weighted eigenvalue problem of the biased infinity Laplacian * ⋮ Some sharp Sobolev regularity for inhomogeneous infinity Laplace equation in plane ⋮ Viscosity solutions to the infinity Laplacian equation with strong absorptions ⋮ A singular boundary value problem for a degenerate elliptic PDE ⋮ Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian ⋮ Large solutions of a class of degenerate equations associated with infinity Laplacian
Cites Work
- Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
- An efficient derivation of the Aronsson equation
- Another way to say caloric
- Inhomogeneous infinity Laplace equation
- Minimization problems for the functional \(\displaystyle{\sup_x}\, F(x,f(x),f'(x))\). I, II
- Extension of functions satisfying Lipschitz conditions
- EXISTENCE AND COMPARISON RESULTS FOR FULLY NONLINEAR DEGENERATE ELLIPTIC EQUATIONS WITHOUT ZEROTH-ORDER TERM1*
- User’s guide to viscosity solutions of second order partial differential equations
- A tour of the theory of absolutely minimizing functions
- The infinity Laplacian, Aronsson's equation and their generalizations
- Uniqueness of ∞-Harmonic Functions and the Eikonal Equation
- A deterministic‐control‐based approach motion by curvature
- Various Properties of Solutions of the Infinity-Laplacian Equation
- The Euler equation and absolute minimizers of \(L^\infty\) functionals
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