Geodesic
On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data
Izvestiya. Mathematics , Tome 75 (2011) no. 1, pp. 101-156

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We introduce the notions of $T$-solutions and shift $T$-solutions of variational inequalities corresponding to a non-linear degenerate anisotropic elliptic operator, a constraint set in a sufficiently large class, and an $L^1$-right-hand side. We prove theorems on the existence and uniqueness of such solutions and describe their properties. While the notion of $T$-solution is defined only when the constraint set contains at least one bounded function, the notion of shift $T$-solution does not require this condition. We describe the relation between these notions and prove that these types of solutions of a variational inequality coincide with ordinary solutions whenever the right-hand side is sufficiently regular.
Keywords: degenerate anisotropic elliptic variational inequalities, $L^1$-data, shift $T$-solution, existence and uniqueness of solutions.
Mots-clés : $T$-solution 
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     title = {On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_1_a4/}
}
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A. A. Kovalevsky; Yu. S. Gorban. On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data. Izvestiya. Mathematics , Tome 75 (2011) no. 1, pp. 101-156. http://geodesic.mathdoc.fr/item/IM2_2011_75_1_a4/