Nonlinear Liouville theorems for some critical problems on \(H\)-type groups.

DOI10.1016/S0022-1236(03)00138-1zbMath1045.35018MaRDI QIDQ1428446

Francesco Uguzzoni, Andrea Bonfiglioli

Publication date: 29 March 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

semilinear Dirichlet problemsubelliptic Sobolev space

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Degenerate elliptic equations (35J70) Analysis on other specific Lie groups (43A80) Subelliptic equations (35H20)

Related Items (34)

Estimations optimales du noyau de la chaleur sur les groupes de type Heisenberg ⋮ Ostrowski type inequalities on \(H\)-type groups ⋮ Decay estimates for fractional wave equations on \(H\)-type groups ⋮ Unnamed Item ⋮ \(L^p\)-weak regularity and asymptotic behavior of solutions for critical equations with singular potentials on Carnot groups ⋮ Perturbation of Yamabe equation on Iwasawa \(N\) groups in presence of symmetry ⋮ Gradient estimates for the heat kernels in higher dimensional Heisenberg groups ⋮ Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds ⋮ Existence and multiplicity of positive solutions to sub-elliptic systems with multiple critical exponents on Carnot groups ⋮ The optimal constant in the \(L^2\) Folland-Stein inequality on the H-type group ⋮ Keller-Osserman type conditions for differential inequalities with gradient terms on the Heisenberg group ⋮ Nonexistence results for the hyperbolic-type equations on graded Lie groups ⋮ Strichartz inequalities for the wave equation with the full Laplacian on H-type groups ⋮ An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group ⋮ Critical growth problems with singular nonlinearities on Carnot groups ⋮ Semilinear subelliptic problems with critical growth on Carnot groups ⋮ Centered Hardy-Littlewood maximal functions on Heisenberg type groups ⋮ A weighted Trudinger-Moser inequality on \(\mathbb{R}^N\) and its application to Grushin operator ⋮ Yamabe-type equations on Carnot groups ⋮ Improved Sobolev inequalities on groups of Iwasawa type in presence of symmetry ⋮ Gradient estimates for the heat semigroup on \(\mathbb H\)-type groups ⋮ The heat kernel on H-type groups ⋮ Local behavior of solutions to subelliptic problems with Hardy potential on Carnot groups ⋮ Unnamed Item ⋮ Optimal decay of \(p\)-Sobolev extremals on Carnot groups ⋮ Conservations laws for critical Kohn-Laplace equations on the Heisenberg group ⋮ The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of \(F_{4(-20)}\) ⋮ Asymptotic behaviour of solutions for a class of degenerate elliptic critical problems ⋮ Pizzetti's formula for H-type groups ⋮ A Liouville-type Theorem on half-spaces for sub-Laplacians ⋮ Critical problems with Hardy potential on stratified Lie groups ⋮ Liouville type results and a maximum principle for non-linear differential operators on the Heisenberg group ⋮ A Multiplicity Result for a Non-Homogeneous Subelliptic Problem with Sobolev Exponent ⋮ Entire solutions for some critical equations in the Heisenberg group

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