Estimates on Green functions and Schrödinger-type equations for non-symmetric diffusions with measure-valued drifts

DOI10.1016/j.jmaa.2006.10.014zbMath1118.35007arXivmath/0605557OpenAlexW2159451050MaRDI QIDQ881991

Renming Song, Panki Kim

Publication date: 23 May 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605557

zbMATH Keywords

Brownian motiontwo-sided estimatesboundary Harnack principletransition densityKato classLipschitz domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) A priori estimates in context of PDEs (35B45) PDEs with low regular coefficients and/or low regular data (35R05)

Related Items (14)

On combinatorics of Schrödinger perturbations ⋮ Estimates for Dirichlet heat kernels, intrinsic ultracontractivity and expected exit time on Lipschitz domains ⋮ Law of large numbers for branching symmetric hunt processes with measure-valued branching rates ⋮ Brownian motion with singular time-dependent drift ⋮ Fractional nonlinear degenerate diffusion equations on bounded domains. I: Existence, uniqueness and upper bounds. ⋮ The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains ⋮ Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings ⋮ Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions ⋮ Boundary behavior of harmonic functions for truncated stable processes ⋮ Intrinsic ultracontractivity of nonsymmetric diffusions with measure-valued drifts and potentials ⋮ On the Green function and Poisson integrals of the Dunkl Laplacian ⋮ Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains ⋮ On dual processes of non-symmetric diffusions with measure-valued drifts ⋮ Uniform conditional ergodicity and intrinsic ultracontractivity

Cites Work

• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Gaussian bounds for the fundamental solutions of \(\nabla(A\nabla u)+B\nabla u-u_ t=0\)
• Brownian motion with singular drift
• Stability of Martin boundary under non-local Feynman-Kac perturbations
• Sharp bounds on the density, Green function and jumping function of subordinate killed BM
• The boundary behavior of heat kernels of Dirichlet Laplacians
• Comparison of Green functions and harmonic measures for parabolic operators
• Green function estimate for censored stable processes
• General gauge and conditional gauge theorems
• A Harnack inequality for the equation \(\nabla (a \nabla u) + b \nabla u = 0\), when \(| b | \in K_{n+1}\)
• Sharp estimates for the Green function in Lipschitz domains
• Two-sided estimates on the density of Brownian motion with singular drift
• Uniform boundary Harnack principle and generalized triangle property
• Gaugeability and conditional gaugeability
• From Brownian Motion to Schrödinger’s Equation

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