Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in RN
- Lemenant, Antoine
- Milakis, Emmanouil
DOIAbstract
AbstractIn 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′|αN where λ1 (resp. λ1′) is the first Dirichlet eigenvalue of the Laplacian in Ω (resp. Ω′) and |Ω△Ω′| is the Lebesgue measure of the symmetric difference. Here the constant α<1 could be taken arbitrary close to 1 (but strictly less) and C is a constant depending on a lot of parameters including α, dimension N and some geometric properties of the domains
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