Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian

DOI10.1007/s00208-008-0297-1zbMath1190.35127OpenAlexW2063532019WikidataQ109406481 ScholiaQ109406481MaRDI QIDQ1006807

Ryuji Kajikiya, Petri Juutinen, Goro Akagi

Publication date: 26 March 2009

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-008-0297-1

zbMATH Keywords

Cauchy problemcomparison principledegenerate diffusionCauchy-Dirichlet problemdecay rate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Viscosity solutions to PDEs (35D40) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear parabolic equations (35K59)

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Parabolic biased infinity Laplacian equation related to the biased tug-of-war ⋮ A strong minimum principle and large time asymptotics for viscosity solutions to a class of doubly nonlinear possibly degenerate parabolic equations ⋮ An inhomogeneous evolution equation involving the normalized infinity Laplacian with a transport term ⋮ Asymptotics of viscosity solutions to some doubly nonlinear parabolic equations ⋮ Evolution driven by the infinity fractional Laplacian ⋮ Degenerate homogeneous parabolic equations associated with the infinity-Laplacian ⋮ On evolutionary problems with a-priori bounded gradients ⋮ On the viscosity solutions to a degenerate parabolic differential equation ⋮ Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian ⋮ Solutions for equations involving the infinity-Laplacian ⋮ Positive viscosity solutions of a third degree homogeneous parabolic infinity Laplace equation ⋮ Refined Asymptotics for the Infinite Heat Equation with Homogeneous Dirichlet Boundary Conditions ⋮ Statistical exponential formulas for homogeneous diffusion ⋮ Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian

Cites Work

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• \(C^1\) regularity for infinity harmonic functions in two dimensions
• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
• Principal eigenvalue of a very badly degenerate operator and applications
• Another way to say caloric
• Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian
• On the evolution governed by the infinity Laplacian
• Extension of functions satisfying Lipschitz conditions
• On the partial differential equation \(u_ x^ 2 u_{xx} +2u_ x u_ y u_{xy} +u_ y^ 2 u_{yy} = 0\)
• Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness
• User’s guide to viscosity solutions of second order partial differential equations
• Viscosity solutions of nonlinear second-order partial differential equations in hilbert spaces
• An axiomatic approach to image interpolation
• A tour of the theory of absolutely minimizing functions
• Uniqueness of ∞-Harmonic Functions and the Eikonal Equation
• Radial viscosity solutions of the Dirichlet problem for semilinear degenerate elliptic equations

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