Harnack inequality for non-divergence form operators on stratified groups

DOI10.1090/S0002-9947-07-04273-0zbMath1113.35032OpenAlexW1932509575MaRDI QIDQ3425941

Andrea Bonfiglioli, Francesco Uguzzoni

Publication date: 7 March 2007

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04273-0

zbMATH Keywords

Harnack inequalityFundamental solutionGreen functionHörmander vector fieldsanalysis on Carnot groups

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Analysis on other specific Lie groups (43A80) Subelliptic equations (35H20)

Related Items

Global existence and asymptotic behavior of solutions to a semilinear parabolic equation on Carnot groups ⋮ Fundamental solutions for non-divergence form operators on stratified groups ⋮ Heat kernels for non-divergence operators of Hörmander type ⋮ Non-divergence operators structured on homogeneous Hörmander vector fields: heat kernels and global Gaussian bounds ⋮ Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients ⋮ 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 ⋮ Wiener-type tests from a two-sided Gaussian bound ⋮ Pointwise local estimates and Gaussian upper bounds for a class of uniformly subelliptic ultraparabolic operators ⋮ On a non-smooth potential analysis for Hörmander-type operators ⋮ Potential analysis for a class of diffusion equations: a Gaussian bounds approach ⋮ Existence of Infinitely Many Solutions For a Class of Semilinear Subelliptic Equations on Rational Carnot Groups ⋮ Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields ⋮ A Wiener test à la Landis for evolutive Hörmander operators ⋮ The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE

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