Geodesic
Toward the $L^1$-theory of degenerate anisotropic elliptic variational inequalities
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 137-152

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We consider nonlinear elliptic second-order variational inequalities with degenerate (with respect to the spatial variable) and anisotropic coefficients and $L^1$-data. We study the cases where the set of constraints belongs to a certain anisotropic weighted Sobolev space and a larger function class. In the first case, some new properties of $T$-solutions and shift $T$-solutions of the investigated variational inequalities are established. Moreover, the notion of $W^{1,1}$-regular $T$-solution is introduced, and a theorem of existence and uniqueness of such a solution is proved. In the second case, we introduce the notion of $\mathcal T$-solution of the variational inequalities under consideration and establish conditions of existence and uniqueness of such a solution.
Keywords: nonlinear elliptic variational inequalities; anisotropy; degeneration; $L^1$-data; $T$-solution; $\mathcal T$-solution. 
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     author = {A. A. Kovalevsky},
     title = {Toward the $L^1$-theory of degenerate anisotropic elliptic variational inequalities},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {137--152},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a13/}
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A. A. Kovalevsky. Toward the $L^1$-theory of degenerate anisotropic elliptic variational inequalities. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 137-152. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a13/