The Hopf-Lax formula in Carnot groups: a control theoretic approach

DOI10.1007/s00526-013-0627-3zbMath1286.35241OpenAlexW2019303149MaRDI QIDQ2445456

Zoltán M. Balogh, Andrea Calogero, Rita Pini

Publication date: 14 April 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-013-0627-3

zbMATH Keywords

Hamilton-Jacobi equationviscosity solutionCarnot groupsHopf-Lax formula

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Convexity of real functions of several variables, generalizations (26B25) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Sub-Riemannian geometry (53C17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (8)

Extension of mathematical morphology in Riemannian spaces ⋮ Homogenization for sub-riemannian Lagrangians ⋮ Note on the q-logarithmic Sobolev and p-Talagrand inequalities on Carnot groups ⋮ Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group ⋮ Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton--Jacobi Equations ⋮ Ergodic mean field games with Hörmander diffusions ⋮ Non coercive unbounded first order mean field games: the Heisenberg example ⋮ Unnamed Item

Cites Work

• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Functional inequalities and Hamilton-Jacobi equations in geodesic spaces
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Note on the Fenchel transform in the Heisenberg group
• Control theory from the geometric viewpoint.
• Equivalent definitions of \(BV\) space and of total variation on metric measure spaces
• Metric Hopf-Lax formula with semicontinuous data
• Hamilton-Jacobi semigroup on length spaces and applications
• Notion of convexity in Carnot groups
• Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below—The Compact Case
• A VERSION OF THE HOPF-LAX FORMULA IN THE HEISENBERG GROUP
• Hyperbolic systems of conservation laws II
• Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• On Hopf's formulas for solutions of Hamilton-Jacobi equations
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints. I
• The partial differential equation u_t + uu_x = μ_xx
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
• Continuity of optimal control costs and its application to weak KAM theory
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