Comparison of Green functions and harmonic measures for parabolic operators

DOI10.1007/s11118-005-2606-6zbMath1071.31002OpenAlexW1993926619MaRDI QIDQ1781889

Lotfi Riahi

Publication date: 9 June 2005

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

Full work available at URL: https://doi.org/10.1007/s11118-005-2606-6

zbMATH Keywords

harmonic measureGreen functionPoisson kernelparabolic operator

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Boundary behavior of harmonic functions in higher dimensions (31B25) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Second-order parabolic equations (35K10)

Related Items (9)

Two-sided global estimates of the Green's function of parabolic equations ⋮ Estimates for Dirichlet heat kernels, intrinsic ultracontractivity and expected exit time on Lipschitz domains ⋮ Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts ⋮ Law of large numbers for branching symmetric hunt processes with measure-valued branching rates ⋮ Two-sided estimates on Dirichlet heat kernels for time-dependent parabolic operators with singular drifts in \(C^{1,\alpha }\)-domains ⋮ Brownian motion with drift on spaces with varying dimension ⋮ Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains ⋮ A refined Green's function estimate of the time measurable parabolic operators with conic domains ⋮ Generalized principal eigenvalues on \({\mathbb{R}}^d\) of second order elliptic operators with rough nonlocal kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations
• Second order parabolic equations in nonvariational form: Boundary Harnack principle and comparison theorems for nonnegative solutions
• Examples of irregular domains for some hypoelliptic differential operators
• Green function for Schrödinger operator and conditioned Feynman-Kac gauge
• Conditional transformation of drift formula and potential theory for \(\Delta +b(\cdot)\cdot \nabla\)
• The equivalence of certain heat kernel and Green function bounds
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Uniform bounds for quotients of Green functions on \(C^{1,1}\)-domains
• The Green function for uniformly elliptic equations
• Estimates of harmonic measure
• Gaussian bounds for the fundamental solutions of \(\nabla(A\nabla u)+B\nabla u-u_ t=0\)
• Solutions positives et mesure harmonique pour des operateurs paraboliques dans des ouverts ``Lipschitziens. (Positive solutions and harmonic measure for parabolic operators in ``Lipschitz domains)
• A Harnack inequality for the equation \(\nabla (a \nabla u) + b \nabla u = 0\), when \(| b | \in K_{n+1}\)
• The Dirichlet problem for parabolic operators with singular drift terms
• Estimates of Caloric Measure and the Initial-Dirichlet Problem for the Heat Equation in Lipschitz Cylinders
• On Parabolic Measures and Subparabolic Functions
• A Fatou Theorem for the Solution of the Heat Equation at the Corner Points of a Cylinder
• Bounds for the fundamental solution of a parabolic equation
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
• Existence and Representation of Solutions of Parabolic Equations
• Green function bounds and parabolic potentials on a half-space
• Boundary behaviour of positive solutions of second-order parabolic operators with lower-order terms in a half-space

This page was built for publication: Comparison of Green functions and harmonic measures for parabolic operators