Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics

Hinz M, Rozanova-Pierrat A, Teplyaev A (2021)
SIAM Journal on Control and Optimization 59(2): 1007-1032.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Hinz, MichaelUniBi; Rozanova-Pierrat, Anna; Teplyaev, Alexander
Abstract / Bemerkung
We introduce new parametrized classes of shape admissible domains in R-n, n >= 2, and prove that they are compact with respect to the convergence in the sense of characteristic functions, the Hausdorff sense, the sense of compacts, and the weak convergence of their boundary volumes. The domains in these classes are bounded (epsilon, infinity)-domains with possibly fractal boundaries that can have parts of any nonuniform Hausdorff dimension greater than or equal to n - 1 and less than n. We prove the existence of optimal shapes in such classes for maximum energy dissipation in the framework of linear acoustics. A by-product of our proof is the result that the class of bounded (epsilon, infinity)-domains with fixed epsilon is stable under Hausdorff convergence. An additional and related result is the Mosco convergence of Robin-type energy functionals on converging domains.
Stichworte
shape optimization; uniform domains; fractal boundaries; traces; extensions; mixed boundary value problem; Mosco convergence; variational; convergence
Erscheinungsjahr
2021
Zeitschriftentitel
SIAM Journal on Control and Optimization
Band
59
Ausgabe
2
Seite(n)
1007-1032
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2955127

Zitieren

Hinz M, Rozanova-Pierrat A, Teplyaev A. Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics. SIAM Journal on Control and Optimization. 2021;59(2):1007-1032.
Hinz, M., Rozanova-Pierrat, A., & Teplyaev, A. (2021). Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics. SIAM Journal on Control and Optimization, 59(2), 1007-1032. https://doi.org/10.1137/20M1361687
Hinz, M., Rozanova-Pierrat, A., and Teplyaev, A. (2021). Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics. SIAM Journal on Control and Optimization 59, 1007-1032.
Hinz, M., Rozanova-Pierrat, A., & Teplyaev, A., 2021. Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics. SIAM Journal on Control and Optimization, 59(2), p 1007-1032.
M. Hinz, A. Rozanova-Pierrat, and A. Teplyaev, “Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics”, SIAM Journal on Control and Optimization, vol. 59, 2021, pp. 1007-1032.
Hinz, M., Rozanova-Pierrat, A., Teplyaev, A.: Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics. SIAM Journal on Control and Optimization. 59, 1007-1032 (2021).
Hinz, Michael, Rozanova-Pierrat, Anna, and Teplyaev, Alexander. “Non-Lipschitz Uniform Domain Shape Optimization in Linear Acoustics”. SIAM Journal on Control and Optimization 59.2 (2021): 1007-1032.

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