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On the BBM-Phenomenon in Fractional Poincaré–Sobolev Inequalities with Weights
Hurri-Syrjänen, Ritva; Martínez-Perales, Javier C.; Pérez, Carlos; Vähäkangas, Antti V. (Oxford University Press (OUP), 2023)In this paper, we unify and improve some of the results of Bourgain, Brezis, and Mironescu and the weighted Poincaré–Sobolev estimate by Fabes, Kenig, and Serapioni. More precisely, we get weighted counterparts of the ... -
The Hajłasz Capacity Density Condition is Self-improving
Canto, Javier; Vähäkangas, Antti V. (Springer Science and Business Media LLC, 2022)We prove a self-improvement property of a capacity density condition for a nonlocal Hajłasz gradient in complete geodesic spaces with a doubling measure. The proof relates the capacity density condition with boundary ... -
Fully reliable a posteriori error control for evolutionary problems
Matculevich, Svetlana (University of Jyväskylä, 2015) -
A parallel domain decomposition method for the Helmholtz equation in layered media
Heikkola, Erkki; Ito, Kazufumi; Toivanen, Jari (Society for Industrial and Applied Mathematics, 2019)An efficient domain decomposition method and its parallel implementation for the solution of the Helmholtz equation in three-dimensional layered media are considered. A modified trilinear finite element discretization ... -
Maximal function estimates and self-improvement results for Poincaré inequalities
Kinnunen, Juha; Lehrbäck, Juha; Vähäkangas, Antti; Zhong, Xiao (Springer Berlin Heidelberg, 2019)Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, ...