Weighted Poincaré inequalities for Hörmander vector fields and local regularity for a class of degenerate elliptic equations

DOI10.1007/BF01053453zbMath0841.46018OpenAlexW4249286902MaRDI QIDQ1902484

Richard L. Wheeden, Bruno Franchi, Guozhen Lu

Publication date: 22 November 1995

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01053453

zbMATH Keywords

vector fieldsweighted Poincaré inequalitiesdegenerate elliptic equations with measurable coefficients are givenHörmander rank condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Degenerate elliptic equations (35J70)

Related Items

\(L^{p}\)-estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth ⋮ Fundamental solutions for non-divergence form operators on stratified groups ⋮ Degenerate elliptic operators in one dimension ⋮ Partial Gaussian bounds for degenerate differential operators ⋮ Harnack's inequality on homogeneous spaces ⋮ Harnack estimates for degenerate parabolic equations modeled on the subelliptic \(p\)-Laplacian ⋮ A Poincare's inequality with non-uniformly degenerating gradient ⋮ Relaxation for Dirichlet problems involving a Dirichlet form ⋮ Harnack's inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients ⋮ Nonlinear subelliptic Schrödinger type problems ⋮ Higher-order multilinear Poincaré and Sobolev inequalities in Carnot groups ⋮ 𝐿^{𝑝} estimates for nonvariational hypoelliptic operators with 𝑉𝑀𝑂 coefficients ⋮ Levi’s parametrix for some sub-elliptic non-divergence form operators ⋮ Relaxed Dirichlet problem for the subelliptic \(p\)-Laplacian ⋮ Harnack inequality for non-divergence form operators on stratified groups ⋮ A sharp subelliptic Sobolev embedding theorem with weights

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Hypoelliptic differential operators and nilpotent groups
• Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
• Sobolev and isoperimetric inequalities for degenerate metrics
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
• Analysis on geodesic balls of sub-elliptic operators
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• Hypoelliptic second order differential equations
• Weighted Poincare and Sobolev Inequalities and Estimates for Weighted Peano Maximal Functions
• Hardy-Littlewood inequality for quasiregular mappings in certain domains in R^n
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
• Regularity for quasilinear second‐order subelliptic equations
• Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces
• Harnack's Inequality for Sum of Squares of Vector Fields Plus a Potential
• Weighted sobolev-poincaré inequalities for grushin type operators