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Constrained optimal rearrangement proble...

Mikayelyan, Hayk...

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Constrained optimal rearrangement problem leading to a new type obstacle problem by Mikayelyan, Hayk ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	08-08-2023
Summary	We consider a new type of obstacle problem in the cylindrical domain $\Omega=D\times (0,1)$ arising from minimization of the functional $$ \int_\Omega \frac{1}{2}\|\nabla u\|^2+\chi_{\{v>0\}}udx, $$ where $v(x')=\int_0^1 u(x', t) dt $. We prove several existence and regularity results and show that the comparison principle does not hold for minimizers. This problem is derived from a classical optimal rearrangement problem in a cylindrical domain, under the constraint that the force function does not depend on the $x_n$ variable of the cylindrical axis. A mistake in the Theorem 4.2 of the previous version has been found. The statement remains an open problem.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1606.03174

Citation

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AMA 11th EditionReferences

Mikayelyan, Hayk. Constrained optimal rearrangement problem leading to a new type obstacle problem. Australian National University. August 08, 2023. Accessed October 01, 2025. https://online.provdatabase.com/cite/13182

APA 7th EditionReferences

Mikayelyan, Hayk. (2023). Constrained optimal rearrangement problem leading to a new type obstacle problem. Australian National University. https://online.provdatabase.com/cite/13182

Chicago 17th EditionReferences

Mikayelyan, Hayk. Constrained optimal rearrangement problem leading to a new type obstacle problem. Australian National University. 2023. https://online.provdatabase.com/cite/13182

HarvardReferences

Mikayelyan, Hayk. (2023). Constrained optimal rearrangement problem leading to a new type obstacle problem. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/13182. (Accessed 01 October 2025).

Harvard AustraliaReferences

Mikayelyan, Hayk, 2023, Constrained optimal rearrangement problem leading to a new type obstacle problem, Australian National University, viewed 01 October 2025, <https://online.provdatabase.com/cite/13182>

MLA 9th EditionWorks Cited

Mikayelyan, Hayk. Constrained optimal rearrangement problem leading to a new type obstacle problem. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/13182.

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