Dirichlet problems for linear and semilinear sub-Laplace equations on Carnot groups

DOI10.1186/1029-242X-2012-136zbMath1279.35024WikidataQ59290018 ScholiaQ59290018MaRDI QIDQ372197

Zixia Yuan, Guanxiu Yuan

Publication date: 14 October 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemPerron methodCarnot groupmonotone iteration schemesub-Laplace equation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70)

Related Items (3)

Subelliptic equations with singular nonlinearities on the Heisenberg group ⋮ Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups ⋮ A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group

Cites Work

• Wiener criterion for a class of degenerate elliptic operators
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Supersolutions, monotone iterations, and stability
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups.
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• Positive solutions of Yamabe-type equations on the Heisenberg group
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type
• Boundary element monotone iteration scheme for semilinear elliptic partial differential equations

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