Two-sided eigenvalue estimates for subordinate processes in domains

By Zhen-Qing Chen, Renming Song. 2005

147 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2449fd960a532f5ed7037f0c79d3e37bff40cb80

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In Numerical Analysis

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Citations in the corpus

Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains (2014, background): “[17], and the corresponding eigenfunctions are only known to be Hölder continuous up to the boundary cf.”
What is the fractional Laplacian? A comparative review with new results (2018, methodology): “For example, estimates for eigenvalues of the spectral Laplacian were derived using probabilistic techniques in [95].”
Distributed-order fractional diffusions on bounded domains (2009, result): “Some results for this case are available in Chen and Song [12], Chen et al. [13] and Song and Vondrac̆ek [46].”
Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, methodology): “A number of methods to study this one-dimensional case, and more general cases, were developed by several authors [1], [2], [3], [4], [5], [7], [13], [14], [24], [25], [26], [27], [28], [29], [32], [36].”
On Fractional Laplacians (2013, methodology): “In [6] this result was obtained with ≥ sign by using considerably more complicated techniques.”
Potential theory of subordinate Brownian motions revisited (2011, background): “A third notable omission is the spectral theory for killed subordinate Brownian motions developed in [17, 18, 19].”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “It is proved that the eigenvalues of the RFL are smaller than the ones of SFL: λj ≤ λj for all j ≥ 1, [87].”
Trace estimates for stable processes (2007, methodology): “2) We refer the reader to the papers [24] and [13] for many of the basic probabilistic and analytic properties of the processes X̃D t and its transition probabilities.”
Dirichlet heat kernel estimates for Δα/2 + Δβ/2 (2010, background): “1(i) and some elementary facts from the spectral theory of compact self-adjoint operators and the estimates of eigenvalues established in [15].”
Fractional calculus for power functions and eigenvalues of the fractional Laplacian (2012, methodology): “A number of methods to study this one-dimensional case, and more general cases, were developed by several authors [1], [2], [3], [4], [5], [7], [13], [14], [24], [25], [26], [27], [28], [29], [32], [36].”