On Kelvin Transformation

By Krzysztof Bogdan, Tomás Zák. 2006

70 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/014c660e226bb21fe57f9add58c172c9c82b760f

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Heat kernel estimates for the fractional Laplacian with Dirichlet conditions (2009, background): “By [18], Lemma 4, for x, y ∈ R, G{0}c (x, y) = cα(|y|α−1 + |x|α−1 − |y − x|α−1).”
Getting Acquainted with the Fractional Laplacian (2017, unknown): “[19] (see also Lemma 2.”
The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary (2012, background): “The fractional Kelvin transform has been studied thoroughly in [5].”
Estimates and structure of α-harmonic functions (2006, background): “eenian 4 unless U = R. The Green function and the harmonic measure of the fractional Laplacian are deﬁned in [34, Theorem IV.4.16, pp. 229, 240], see also [8], [7, pp. 191, 250, 384], [31], and [38], [17] for the case of dimension one. We will brieﬂy indicate the following crucial properties. If U i”
Nonexistence results for a class of fractional elliptic boundary value problems (2012, methodology): “We note that, unlike in the present paper, probabilistic techniques are used in [4].”
Ten equivalent definitions of the fractional laplace operator (2015, background): “Various results are also known for the restriction of L to a domain: detailed properties of L in a domain with Dirichlet condition can be found in [8, 9, 10, 11, 33, 38]; see also [6] for the study of L in a domain with certain reflection.”
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian (2005, methodology): “We refer to [ 19 ] for more information and references on the case d = 1 ≤ �.”
Fractional Laplace Operator and Meijer G-function (2015, unknown): “(d) Similar results are easily found for half-space and for the complement of the unit ball by means of Kelvin transformation, see [5, 17, 20] (e) The results for functions supported in the full space R are more rare: a formula for (−∆)α/2f(x) is known when f(x) = e (Fourier transform), f(x) = |x|−a”