Cylindrical optimal rearrangement problem leading to a new type obstacle problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 859-872.

An optimal rearrangement problem in a cylindrical domain Ω = D × ( 0 , 1 ) is considered, under the constraint that the force function does not depend on the x n variable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain

Δ u ( x ' , x n ) = χ { v > 0 } ( x ' ) + χ { v = 0 } ( x ' ) ν u ( x ' , 0 ) + ν u ( x ' , 1 ) l

arising from minimization of the functional

Ω 1 2 u ( x ) 2 + χ { v > 0 } ( x ' ) u ( x ) d x ,

where v ( x ' ) = 0 1 u ( x ' , t ) d t , and ν u is the exterior normal derivative of u at the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.

DOI : 10.1051/cocv/2017047
Classification : 35R35, 49J20
Mots clés : Obstacle problem, rearrangements
Mikayelyan, Hayk 1

1
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Mikayelyan, Hayk. Cylindrical optimal rearrangement problem leading to a new type obstacle problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 859-872. doi : 10.1051/cocv/2017047. http://www.numdam.org/articles/10.1051/cocv/2017047/

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