The ``ergodic limit for a viscous Hamilton-Jacobi equation with Dirichlet conditions

DOI10.4171/RLM/561zbMath1189.35102MaRDI QIDQ966208

Alessio Porretta

Publication date: 23 April 2010

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/journal.php?jrn=rlm

zbMATH Keywords

blow-upviscous Hamilton-Jacobi equationsergodic limit

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Semilinear elliptic equations (35J61) Blow-up in context of PDEs (35B44) Viscosity solutions to PDEs (35D40) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (18)

Quasilinear elliptic problems with singular and homogeneous lower order terms ⋮ Large solutions and gradient bounds for quasilinear elliptic equations ⋮ Existence issues for a large class of degenerate elliptic equations with nonlinear Hamiltonians ⋮ A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems ⋮ On the comparison principle for unbounded solutions of elliptic equations with first order terms ⋮ Existence and multiplicity for an elliptic problem with critical growth in the gradient and sign-changing coefficients ⋮ Ergodic pairs for singular or degenerate fully nonlinear operators ⋮ A priori estimates for non-coercive Dirichlet problems with subquadratic gradient terms ⋮ Isoperimetric inequalities for an ergodic stochastic control problem ⋮ Unnamed Item ⋮ Some existence results for a quasilinear problem with source term in Zygmund-space ⋮ Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control ⋮ Multiplicity results in the non-coercive case for an elliptic problem with critical growth in the gradient ⋮ Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem ⋮ Ergodic pairs for degenerate pseudo Pucci's fully nonlinear operators ⋮ Unnamed Item ⋮ Multiplicity of solutions for a class of elliptic problem of \(p\)-Laplacian type with a \(p\)-gradient term ⋮ \({\mathcal{C}}^{1, \gamma }\) regularity for singular or degenerate fully nonlinear equations and applications

Cites Work

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• Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I: The model problem
• Criteria of solvability for multidimensional Riccati equations
• Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions
• Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms
• Asymptotic Behaviour of the Gradient of Large Solutions to Some Nonlinear Elliptic Equations
• Weak Solutions of Some Quasilinear Elliptic Equations with Data Measures
• Invariant criteria for existence of solutions to second-order quasilinear elliptic equations
• On ergodic stochastic control
• Comparison and Existence Results for Classes of Nonlinear Elliptic Equations with General Growth in the Gradient

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