Boundary Harnack principle and Martin boundary for a uniform domain

By Hiroaki Aikawa. 2001

131 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f260ae3259fcc235017fafefdfc84d093909d0a6

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Boundary Harnack Principle for p-harmonic Functions in Smooth Euclidean Domains (2007, background): “In [1], the first named author showed that a uniform domain satisfies a local version of the boundary Harnack principle which is stronger than the above boundary Harnack principle.”
Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in $L^p$ (2012, background): “ements. The ﬁrst named author wishes to thank John Lewis for helpful comments concerning the paper [BL]. He also thanks Misha Safonov and Tatiana Toro for bringing to our attention the work of Aikawa [Ai1], [Ai2]. 2. Outline of the Strategy of the Proof Let us sketch the strategy of the proofs of Th”
Uniform boundary Harnack principle and generalized triangle property (2005, methodology): “Suppose that D is a uniform domain (see for example [ Aik01 , p.120]), i.e., that there exists a constant c > 0 such that each pair of points x1,x2 2 D can be connected by a rectifiable curve i in D for which”
Neumann and Dirichlet Heat Kernels in Inner Uniform Domains (2011, methodology): “We were delighted to discover in [1] the results and techniques we needed for our purpose.”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “• When α ∈ [1, 2), X is the closure of an open set with C-smooth boundary for some β > α−1, and ν(x, y) = c|x−y|−k−α, then one can take D to be the class of C∞ c (R ) functions with normal derivative vanishing everywhere on the boundary of X (see [45, Theorem 6.”
Rectifiability of harmonic measure (2015, methodology): “f the difﬁculties of Theorem 1.1 is due to the fact that the non-Ahlfors regularity of ∂Ω makes it difﬁcult to apply some usual tools from potential of theory, such as the ones developed by Aikawa in [Ai1] and [Ai2]. In our proof we solve this issue by applying some stopping time arguments involving”