On improvement of summability properties in nonautonomous Kolmogorov equations

DOI10.3934/cpaa.2014.13.1237zbMath1284.35210arXiv1207.1293OpenAlexW2963734139MaRDI QIDQ2438951

Luca Lorenzi, Luciana Angiuli

Publication date: 7 March 2014

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1293

zbMATH Keywords

unbounded coefficientsultracontractivityHarnack type inequalityevolution systems of measuressupercontractivityultraboundedness

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Invariant measures for infinite-dimensional dissipative dynamical systems (37L40)

Related Items (8)

Pointwise gradient estimates for evolution operators associated with Kolmogorov operators ⋮ Hypercontractivity, supercontractivity, ultraboundedness and stability in semilinear problems ⋮ Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions ⋮ On the Dirichlet and Neumann evolution operators in \(\mathbb R_+^d\) ⋮ INVARIANT MEASURES FOR SYSTEMS OF KOLMOGOROV EQUATIONS ⋮ \(L^{p}\)-estimates for parabolic systems with unbounded coefficients coupled at zero and first order ⋮ Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite-dimensional convex domains ⋮ Harnack inequalities with power \(\pmb{p\in (1,+\infty )}\) for transition semigroups in Hilbert spaces

Cites Work

• Pointwise gradient estimates for evolution operators associated with Kolmogorov operators
• Ultraboundedness for parabolic equations in convex domains without boundary conditions
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Upper bounds for symmetric Markov transition functions
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• Some remarks on ultracontractivity
• Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter
• Functional inequalities for empty essential spectrum
• The free Markoff field
• Compactness and invariance properties of evolution operators associated with Kolmogorov operators with unbounded coefficients
• Compactness and Asymptotic Behavior in Nonautonomous Linear Parabolic Equations with Unbounded Coefficients in ℝ d
• Nonautonomous Kolmogorov parabolic equations with unbounded coefficients
• Invariant measures and maximal L ² regularity for nonautonomous Ornstein-Uhlenbeck equations
• Logarithmic Sobolev Inequalities
• Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
• A character of the gradient estimate for diffusion semigroups
• Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations

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