Second Domain Variation for Problems with Robin Boundary Conditions

Catherine Bandle () and Alfred Wagner ()
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Catherine Bandle: Universität Basel
Alfred Wagner: RWTH Aachen

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 2, No 2, 430-463

Abstract: Abstract In this paper, the first and second domain variations for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions are computed. Extremal properties of the ball among nearly spherical domains of given volume are derived. The discussion leads to a Steklov eigenvalue problem. As a by-product, a general characterization of the optimal shapes is obtained.

Keywords: Robin boundary value problem; Optimal domain; First domain variation; Second domain variation; Steklov eigenvalue; 49K20; 49J20; 34L15; 35J20; 35N25 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-015-0801-1

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