Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
-
Bin Qian
and
Beibei Zhang
Abstract
In this paper, we obtain the reverse Bakry–Émery-type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang–Harnack inequality, Hamilton’s gradient estimate and Liouville property are also presented by the reverse logarithmic Sobolev inequality.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11671076
Funding statement: Sponsored by the National Natural Science Foundation of China (No. 11671076).
Acknowledgements
The authors would like to express sincere thanks to the anonymous referee for his/her value suggestion and comment which greatly improve the quality of the paper.
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
Articles in the same Issue
- Frontmatter
- Rings of differential operators on (k,s)-th Tjurina algebras of singularities
- Cokernels of random matrix products and flag Cohen–Lenstra heuristic
- Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling
- The L p -L q compactness of commutators of oscillatory singular integrals
- Determination of a pair of newforms from the product of their twisted central values
- Metrical properties of exponentially growing partial quotients
- Nonlinear operations and factorizations on a class of affine modulation spaces
- On algebraic degrees of certain exponential sums over finite fields
- The ranks of (a,b)-Fibonacci sequences and congruences for certain partition functions and Ramanujan's mock theta functions
- Dynamics of radial threshold solutions for generalized energy-critical Hartree equation
- Modular representations of GL2(𝔽𝑞) using calculus
- Bounding the number of p'-degree characters from below
- Existence and multiplicity of non-radial sign-changing solutions for a semilinear elliptic equation in hyperbolic space
- Duality theorems for polyanalytic functions
- Lower bounds for the number of number fields with Galois group GL2(𝔽ℓ)
- Cylindrical ample divisors on Du Val del Pezzo surfaces
