A VERSION OF THE HOPF-LAX FORMULA IN THE HEISENBERG GROUP

DOI10.1081/PDE-120004897zbMath1080.49023MaRDI QIDQ3149955

Bianca Stroffolini, Juan J. Manfredi

Publication date: 2002

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

zbMATH Keywords

Heisenberg groupHamilton-Jacobi equationsviscosity solutionssubelliptic equations

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Analysis on real and complex Lie groups (22E30) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

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Extension of mathematical morphology in Riemannian spaces ⋮ Weakly coupled systems of fully nonlinear parabolic equations in the Heisenberg group ⋮ Existence results for the fractional Q-curvature problem on three dimensional CR sphere ⋮ Unnamed Item ⋮ Homogenization for sub-riemannian Lagrangians ⋮ PDE-based group equivariant convolutional neural networks ⋮ Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group ⋮ The Hopf-Lax formula in Carnot groups: a control theoretic approach ⋮ Functional inequalities and Hamilton-Jacobi equations in geodesic spaces ⋮ Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group ⋮ Subelliptic Hamilton-Jacobi equations: the coercive evolution case ⋮ Geometric inequalities on Heisenberg groups ⋮ Evolution equations on Gabor transforms and their applications ⋮ Almost periodic viscosity solutions of nonlinear evolution equations in Carnot groups ⋮ Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations ⋮ Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton--Jacobi Equations ⋮ Morphological and linear scale spaces for fiber enhancement in DW-MRI ⋮ Taylor formula for homogeneous groups and applications ⋮ Homogenization of Hamilton-Jacobi equations in Carnot Groups

Cites Work

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• Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient
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• Balls and metrics defined by vector fields. I: Basic properties
• A remark on regularization in Hilbert spaces
• Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions
• Existence of viscosity solutions of Hamilton-Jacobi equations
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• On Hopf's formulas for solutions of Hamilton-Jacobi equations
• Regularity of quasi-linear equations in the Heisenberg group
• Hopf-Lax formulas for semicontinuous data
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

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