Browsing Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics by Author "Lemenant, A."
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Article
On the extension property of reifenberg-flat domains
Lemenant, A.; Milakis, E.; Spinolo, L. V. (2014)We provide a detailed proof of the fact that any open set whose boundary is sufficiently flat in the sense of Reifenberg is also Jones-flat, and hence it admits an extension operator. We discuss various applications of ...
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Article
Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in RN
Lemenant, A.; Milakis, E. (2010)In this paper we prove that if Ω and Ω′ are close enough for the complementary Hausdorff distance and their boundaries satisfy some geometrical and topological conditions then| λ1 - λ1′ | ≤ C | Ω △ Ω′ |frac(α, N) where λ1 ...
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Article
Spectral stability estimates for the Dirichlet and Neumann Laplacian in rough domains
Lemenant, A.; Milakis, E.; Spinolo, L. V. (2013)In this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the Neumann and the Dirichlet Laplacian. Our main results follow from an abstract lemma ...
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Article
A stability result for nonlinear Neumann problems in reifenberg flat domains in Rn
Lemenant, A.; Milakis, E. (2011)In this paper we prove that if ωk is a sequence of Reifenberg-flat domains in RN that converges to ω for the complementary Haus- dorff distance and if in addition the sequence ωk has a "uniform size of holes", then the ...