Optimizing the first Dirichlet eigenvalue of the Laplacian with an obstacle
نویسندگان
چکیده
منابع مشابه
The ∞−Laplacian first eigenvalue problem
We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In section 5 we make some remarks on the simplicity of the first eigenvalue of ∆∞: this will be the object of a join...
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15 صفحه اولBlaschke-santaló and Mahler Inequalities for the First Eigenvalue of the Dirichlet Laplacian
For K belonging to the class of convex bodies in R, we consider the λ1product functional, defined by λ1(K)λ1(K ), where K is the polar body of K, and λ1(·) is the first Dirichlet eigenvalue of the Dirichlet Laplacian. As a counterpart of the classical Blaschke-Santaló inequality for the volume product, we prove that the λ1product is minimized by balls. Much more challenging is the problem of ma...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2019
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201702_003