A Class of Sub-elliptic Equations on the Heisenberg Group and Related Interpolation Inequalities

DOI10.1007/978-3-0348-0516-2_7zbMath1262.35208OpenAlexW20120751MaRDI QIDQ4912913

Eugénio M. Rocha, Jianqing Chen

Publication date: 28 March 2013

Published in: Advances in Harmonic Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0516-2_7

zbMATH Keywords

least energy solutionsGagliardo-Nirenberg inequality

Mathematics Subject Classification ID

Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (7)

Critical Gagliardo–Nirenberg, Trudinger, Brezis–Gallouet–Wainger inequalities on graded groups and ground states ⋮ Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups ⋮ Limiting cases of Sobolev inequalities on stratified groups ⋮ Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and \(p\)-sub-Laplacian systems ⋮ Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity ⋮ Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations ⋮ Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

Cites Work

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• Two-sided Hardy-type inequalities for monotone functions
• A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group
• Best constant in weighted Sobolev inequality with weights being powers of distance from the origin
• Boundedness of classical operators on classical Lorentz spaces
• The Weighted Hardy's Inequality for Nonincreasing Functions
• Integral Operators on the Cone of Monotone Functions
• Non-existence results for semilinear kohn-laplace equations in unbounded domains
• Weighted Hardy Inequalities for Increasing Functions
• Two-sided Hardy-type inequalities for monotone functions
• Equivalence of Hardy-type inequalities with general measures on the cones of non-negative respective non-increasing functions
• Characterisation of Embeddings in Lorentz Spaces
• Critical semilinear equations on the Heisenberg group: the effect of the topology of the domain

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