A curious equation involving the ∞-Laplacian

DOI10.1515/ACV.2010.017zbMath1200.49026arXiv0902.1771WikidataQ110085982 ScholiaQ110085982MaRDI QIDQ3053239

Teemu Lukkari, Peter Lindqvist

Publication date: 4 November 2010

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.1771

zbMATH Keywords

viscosity solutioncomparison principleHarnack's inequalityvariable exponentCaccioppoli estimate\(\infty\)-Laplacian

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Optimality conditions for minimax problems (49K35) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (11)

The asymptotic behaviour of the \(p(x)\)-Laplacian Steklov eigenvalue problem ⋮ Harnack's inequality and the strong \(p(\cdot )\)-Laplacian ⋮ The Robin eigenvalue problem for the \(p(x)\)-Laplacian as \(p\to \infty \) ⋮ On the continuity of the Luxemburg norm of the gradient in $L^{p(\cdot )}$ with respect to $p(\cdot )$ ⋮ Maximal operators for the \(p\)-Laplacian family ⋮ \(\Gamma \)-convergence of power-law functionals with variable exponents ⋮ The limit as \(p(x)\rightarrow \infty \) of solutions to the inhomogeneous Dirichlet problem of the \(p(x)\)-Laplacian ⋮ A limiting free boundary problem with gradient constraint and tug-of-war games ⋮ 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 ⋮ Minimization of quotients with variable exponents

Cites Work

• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• The \(\infty\)-eigenvalue problem
• Extension of functions satisfying Lipschitz conditions

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