Publisher DOI: 10.1007/s10915-018-0806-7
Title: Optimal Shape Design for the p-Laplacian Eigenvalue Problem
Language: English
Authors: Mohammadi, Seyyed Abbas 
Bozorgnia, Farid 
Voß, Heinrich 
Keywords: Eigenvalue optimization; p-Laplacian; Rearrangement algorithm
Issue Date: 15-Feb-2019
Source: Journal of Scientific Computing 78 (2): 1231-1249 (2019-02-15)
Abstract (english): 
In this paper, a shape optimization problem corresponding to the p-Laplacian operator is studied. Given a density function in a rearrangement class generated by a step function, find the density such that the principal eigenvalue is as small as possible. Considering a membrane of known fixed mass and with fixed boundary of prescribed shape consisting of two different materials, our results determine the way to distribute these materials such that the basic frequency of the membrane is minimal. We obtain some qualitative aspects of the optimizer and then we determine nearly optimal sets which are approximations of the minimizer for specific ranges of parameters values. A numerical algorithm is proposed to derive the optimal shape and it is proved that the numerical procedure converges to a local minimizer. Numerical illustrations are provided for different domains to show the efficiency and practical suitability of our approach.
ISSN: 0885-7474
Journal: Journal of scientific computing 
Institute: Mathematik E-10 
Document Type: Article
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