AN ANISOTROPIC INFINITY LAPLACIAN OBTAINED AS THE LIMIT OF THE ANISOTROPIC (p, q)-LAPLACIAN

DOI10.1142/S0219199711004543zbMath1236.35028MaRDI QIDQ3110884

Mayte Pérez-Llanos, Julio D. Rossi

Publication date: 16 January 2012

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

viscosity solutions\((p,q)\)-Laplacianinfinity-Laplacian

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20) Viscosity solutions to PDEs (35D40)

Related Items (4)

Comparison principles for second-order elliptic/parabolic equations with discontinuities in the gradient compatible with Finsler norms ⋮ An eigenvalue problem involving an anisotropic differential operator ⋮ The behavior of solutions to an elliptic equation involving a \(p\)-Laplacian and a \(q\)-Laplacian for large \(p\) ⋮ Anisotropic torsional creep problems involving rapidly growing differential operators

Cites Work

• The Neumann problem for the \(\infty\)-Laplacian and the Monge--Kantorovich mass transfer problem
• Tug-of-war with noise: a game-theoretic view of the \(p\)-Laplacian
• Overview of differential equations with non-standard growth
• The limit as \(p(x)\rightarrow \infty \) of solutions to the inhomogeneous Dirichlet problem of the \(p(x)\)-Laplacian
• \(p(x)\)-harmonic functions with unbounded exponent in a subdomain
• The behaviour of the \(p(x)\)-Laplacian eigenvalue problem as \(p(x)\rightarrow \infty \)
• Limits as \(p(x)\rightarrow \infty \) of \(p(x)\)-harmonic functions
• On the higher eigenvalues for the \(\infty\)-eigenvalue problem
• The \(\infty\)-eigenvalue problem
• Existence and nonexistence results for anisotropic quasilinear elliptic equations
• On Fully Nonlinear PDEs Derived from Variational Problems ofL^pNorms
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• EXISTENCE AND COMPARISON RESULTS FOR FULLY NONLINEAR DEGENERATE ELLIPTIC EQUATIONS WITHOUT ZEROTH-ORDER TERM1*
• Tug-of-war and the infinity Laplacian
• Optimal regularity for the pseudo infinity Laplacian
• User’s guide to viscosity solutions of second order partial differential equations
• An axiomatic approach to image interpolation
• A tour of the theory of absolutely minimizing functions
• The pseudo-p-Laplace eigenvalue problem and viscosity solutions asp→ ∞

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