About Hölder-regularity of the convex shape minimizing 2
نویسنده
چکیده
In this paper, we consider the well-known following shape optimization problem: λ2(Ω ∗) = min |Ω|=V0 Ω convex λ2(Ω), where λ2(Ω) denotes the second eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions in Ω ⊂ R, and |Ω| is the area of Ω. We prove, under some technical assumptions, that any optimal shape Ω∗ is C 1 2 and is not C for any α > 1 2 . We also derive from our strategy some more general regularity results, in the framework of partially overdetermined boundary value problems, and we apply these results to some other shape optimization problems.
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