Local solvability of linear differential operators with double characteristics II: Sufficient conditions for left-invariant differential operators of order two on the Heisenberg group

DOI10.1515/CRELLE.2007.044zbMath1215.35014OpenAlexW1990612744MaRDI QIDQ5421669

Detlef Müller

Publication date: 24 October 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2007.044

zbMATH Keywords

second order differential operatorsleft-invariant vector fieldsSjöstrand's cone condition

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Nilpotent and solvable Lie groups (22E25) Analysis on other specific Lie groups (43A80) Hypoelliptic equations (35H10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Local solvability of some partial differential operators with non-smooth coefficients ⋮ On the Solvability of a Class of Second Order Degenerate Operators ⋮ Uniqueness of solutions to Schrödinger equations on 2-step nilpotent Lie groups

Cites Work

• Analysis of second order differential operators on Heisenberg groups. I
• On the solvability of homogeneous left-invariant differential operators on the Heisenberg group
• Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition
• Analysis of second order differential operators on Heisenberg groups. II
• Symplectic classification of quadratic forms, and general Mehler formulas
• Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups
• Local solvability for positive combinations of generalized sub-Laplacians on the Heisenberg group
• A class of solvable non-homogeneous differential operators on the Heisenberg group
• An Example in the Solvability Theory of Linear PDE's
• Non-solvability for a class of left-invariant second-order differential operators on the Heisenberg group
• Parametrices for pseudodifferential operators with multiple characteristics

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