On the best possible character of the 𝐿^{𝑄} norm in some a priori estimates for non-divergence form equations in Carnot groups

DOI10.1090/S0002-9939-03-07105-3zbMath1036.35047MaRDI QIDQ4417250

Nicola Garofalo, Donatella Danielli, Duy-Minh Nhieu

Publication date: 28 July 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemAlexandrov-Bakelman-Pucci estimategeometric maximum principle\(\infty\)-horizontal Laplacianhorizontal Monge-Ampère equation

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) Analysis on real and complex Lie groups (22E30) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (13)

Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations ⋮ The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations ⋮ The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics ⋮ Hölder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group ⋮ Harnack inequality for a subelliptic PDE in nondivergence form ⋮ Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions ⋮ Harnack’s inequality for a class of non-divergent equations in the Heisenberg group ⋮ Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities ⋮ Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces ⋮ The Hardy inequality and nonlinear parabolic equations on Carnot groups ⋮ New properties of convex functions in the Heisenberg group ⋮ Some a priori estimates for a class of operators in the Heisenberg group ⋮ A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups

Cites Work

• Unnamed Item
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• Subelliptic estimates and function spaces on nilpotent Lie groups
• \(H\)-type groups and Iwasawa decompositions
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• Sub-Riemannian geometry. Proceedings of the satellite meeting of the first European congress of mathematics `Journées nonholonomes: géométrie sous-riemannienne, théorie du contrôle, robotique', Paris, France, June 30--July 1, 1992
• Notion of convexity in Carnot groups
• Limitazioni per soluzioni di equazioni ellittiche
• Operatori ellittice estremanti
• Hypoelliptic second order differential equations
• Sulle equazioni ellittiche del secondo ordine di tipo non variazionale a coefficienti discontinui
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Subadditivity of Homogeneous Norms on Certain Nilpotent Lie Groups
• W 2,p -Solvability of the Dirichlet Problem for Nondivergence Elliptic Equations with VMO Coefficients
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• 𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with 𝑉𝑀𝑂 coefficients
• Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces
• A fundamental solution for a subelliptic operator
• Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations

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