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Full-Text Articles in Physical Sciences and Mathematics
Optimal Solvability For The Dirichlet And Neumann Problem In Dimension Two, Atanas Stefanov, Gregory C. Verchota
Optimal Solvability For The Dirichlet And Neumann Problem In Dimension Two, Atanas Stefanov, Gregory C. Verchota
Mathematics - All Scholarship
We show existence and uniqueness for the solutions of the regularity and the Neumann problems for harmonic functions on Lipschitz domains with data in the Hardy spaces Hp1,(partial D)(Hp (partial D)), p>2/3-E, where D C R2 and E is a (small) number depending on the Lipschitz nature of D. This in turn implies that solutions to the Dirichlet problem with data in the Holder class C1/2+E(partial D) are themselves in C1/2+E(D). Both of these results are sharp. In fact, we prove a more general statement regarding the Hp solvability …
Bounded Point Evaluations And Local Spectral Theory, Abdellatif Bourhim
Bounded Point Evaluations And Local Spectral Theory, Abdellatif Bourhim
Mathematics - All Scholarship
We study in this paper the concept of bounded point evaluations for cyclic operators. We give a negative answer to a question of L.R. Williams Dynamic Systems and Apllications 3(1994) 103-112. Furthermore, we generalize some results of Williams and give a simple proof of theorem 2.5 of L.R. Williams (The Local Spectra of Pure Quasinormal Operators J. Math. anal. Appl. 187(1994) 842-850) that non normal hyponormal weighted shifts have fat local spectra.
Super-Brownian Limits Of Voter Model Clusters, Maury Bramzon, J. Theodore Cox, Jean-Francois Le Gall
Super-Brownian Limits Of Voter Model Clusters, Maury Bramzon, J. Theodore Cox, Jean-Francois Le Gall
Mathematics - All Scholarship
The voter model is one of the standard interacting particle systems. Two related problems for this process are to analyze its behavior, after large times t, for the sets of sites (a) sharing the same opinion as the site 0, and (b) having the opinion that was originally at 0. Results on the sizes of these sets were given in [Sa79] and [BG80]. Here, we investigate the spatial structure of these sets in d ≥ 2, which we show converge to quantities associated with super-Brownian motion, after suitable normalization. The main theorem from [CDP98] serves as an important tool for …