Sharp Estimates for the Green Function in Lipschitz Domains

By Krzysztof Bogdan. 2000

84 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/756ea5c80e63742c839c010a2c7474b627773ae5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

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).”
Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, methodology): “Sharp estimates of the Green function of Lipschitz domains were given in 2000 by Bogdan [6].”
Two‐sided Green function estimates for killed subordinate Brownian motions (2010, methodology): “Since the arguments of Bogdan [3] and Hansen [15] are by now quite standard, we will omit the details of this part.”
Uniform boundary Harnack principle and generalized triangle property (2005, methodology): “In [ Bog00 ], B(x,y) is defined with 3r(x,y) instead of 5r(x,y) in our definition.”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “In fact, resolved cases indicate that sharp estimates of the Green function are equivalent to BHI ([20]), hence not easier to obtain.”
A priori bounds for semilinear equations and a new class of critical exponents for Lipschitz domains (2007, background): “We note that the results of [3] are stated for n 3, but it is clear from the proofs that for n = 2 only the nature of the fundamental singularity changes.”
Estimates and structure of α-harmonic functions (2006, background): “For more information on typical applications we refer the reader to [11], [30], [12], [20], [13], [14], [22], see also [25] for a general perspective.”
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian (2005, methodology): “The estimate was suggested by the sharp estimates of the Green function of Lipschitz domains [38] for the isotropic ν (see also [14]).”
Green function estimate for censored stable processes (2002, result): “Thanks to Theorems 2.7, 2.8 and 3.1, the proof of (3.18) is almost the same as the proof of Proposition 6 and Theorem 2 in Bogdan [ 5 ].”