Uniform boundary Harnack principle and generalized triangle property

By Wolfhard Hansen. 2005

77 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7f3ff27258802102d1a8962e5703817174b2d79f

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “Once we have the interior estimates, we can apply Theorem 2.14 and the boundary Harnack principle (Theorem 2.15), and use the arguments of Bogdan [3] and Hansen [15] to get the full estimates (1.5) for bounded κ-fat open sets D.”
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian (2005, background): “[14, 31 , 21] and Proposition 1 above), and related boundary problems (comp.”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “We expect further progress in this direction with applications to perturbation theory via the so-called 3G theorems, and to nonlinear partial differential equations ([25, 47, 70]).”
Estimates of the Green Function for the Fractional Laplacian Perturbed by Gradient (2010, background): “The so-called 3G Theorem holds for G: G(x, z) ∧ G(z, y) ≤ cG(x, y) , x, y, z ∈ D , where c depends only on d, α and the distortion of D ([25]).”
Estimates and structure of α-harmonic functions (2006, background): “For more information on typical applications we refer the reader to [11–14,20,22,24,30], see also [25] for a general perspective.”
Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators (2007, methodology): “The developments hinge on the various versions of the so-called 3G Theorem for the (unperturbed) Green function of � α/2 , which are obtained from the so-called boundary Harnack principle ([15, 28, 20 ], see, e.g., [14, 2] for the results and references in case of the Laplacian).”