Homogenization and Convergence of Correctors in Carnot Groups

DOI10.1080/03605300500300014zbMath1080.35005OpenAlexW2011540049MaRDI QIDQ5713480

Bruno Franchi, Cristian E. Gutiérrez, Van Truyen Nguyen

Publication date: 14 December 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300500300014

zbMATH Keywords

correctorsMeyer type estimatesStampacchia type operator

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Nilpotent and solvable Lie groups (22E25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (11)

$\Gamma$-Convergence for Functionals Depending on Vector Fields. II. Convergence of Minimizers ⋮ \(L^p\) estimates for weak solutions to nonlinear degenerate parabolic systems ⋮ \( \Gamma\)-convergence for functionals depending on vector fields. I: Integral representation and compactness ⋮ High Contrasting Diffusion in Heisenberg Group: Homogenization of Optimal Control via Unfolding ⋮ The polynomial growth solutions to some sub-elliptic equations on the Heisenberg group ⋮ Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity \(q > 1\) and with natural growth ⋮ Partial regularity for degenerate subelliptic systems associated with Hörmander's vector fields ⋮ Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton--Jacobi Equations ⋮ \( \Gamma \)-convergence and homogenisation for a class of degenerate functionals ⋮ Integral representation of local left-invariant functionals in Carnot groups ⋮ G-convergence of elliptic and parabolic operators depending on vector fields

Cites Work

• Balls and metrics defined by vector fields. I: Basic properties
• \(H\) convergence for quasi-linear elliptic equations with quadratic growth
• Two-scale homogenization in the Heisenberg group
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• Regularity for nonlinear equations involving square Hörmander operators
• Maximum Principle, Nonhomogeneous Harnack Inequality, and Liouville Theorems forX-Elliptic Operators
• A real analysis theorem and applications to homogenization

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