The limit as \(p(x)\rightarrow \infty \) of solutions to the inhomogeneous Dirichlet problem of the \(p(x)\)-Laplacian

DOI10.1016/j.na.2010.05.032zbMath1196.35090OpenAlexW2093277729MaRDI QIDQ988853

Julio D. Rossi, Mayte Pérez-Llanos

Publication date: 19 August 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.05.032

zbMATH Keywords

Dirichlet boundary conditions\(p(x)\)-Laplacian\(\infty \)-Laplacian

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Theoretical approximation in context of PDEs (35A35) Viscosity solutions to PDEs (35D40) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians ⋮ The convergence of nonnegative solutions for the family of problems −Δ_pu=λe^uasp→∞ ⋮ Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces ⋮ On a family of torsional creep problems involving rapidly growing operators in divergence form ⋮ Anisotropic torsional creep problems involving rapidly growing differential operators ⋮ AN ANISOTROPIC INFINITY LAPLACIAN OBTAINED AS THE LIMIT OF THE ANISOTROPIC (p, q)-LAPLACIAN ⋮ On a family of torsional creep problems in Finsler metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• 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
• \(p(x)\)-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
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• On the higher eigenvalues for the \(\infty\)-eigenvalue problem
• The \(\infty\)-eigenvalue problem
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Eigenvalues of the \(p(x)\)-Laplacian Steklov problem
• On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
• A curious equation involving the ∞-Laplacian
• Tug-of-war and the infinity Laplacian
• User’s guide to viscosity solutions of second order partial differential equations
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• An axiomatic approach to image interpolation
• A tour of the theory of absolutely minimizing functions
• Limit Branch of Solutions asp → ∞ for a Family of Sub-Diffusive Problems Related to thep-Laplacian