Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
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引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 4006-4039, June 2024. Abstract. We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains [math] of [math]. Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional [math]-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional [math]-Laplacians and present several simulations that reveal the boundary behavior of solutions.
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SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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