On $ T$-solutions of degenerate anisotropic elliptic variational inequalities with $ L^1$-data

Kovalevsky, Alexander A.; Gorban, Yuliya

doi:10.1070/im2011v075n01abeh002529

Cited by 6 publications

(8 citation statements)

References 30 publications

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“…/ under the fixed value of the second variable. In our case we have no opportunity to use the results [21][22][23] directly. We follow a general approach for proving the above-mentioned theorem.…”

Section: Introductionmentioning

confidence: 99%

“…This approach has been proposed in [1] to the investigation on the existence and properties of solutions for nonlinear elliptic second-order equations with isotropic nondegenerate (with respect to the independent variables) coefficients and L 1 -right-hand sides. In [21,23] this approach has been taken to the anisotropic degenerate case. Also we use some ideas of [24].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the existence results of some other types of solutions to the given problem were also obtained. Observe that the proofs of these theorems are based on use of some results of [21][22][23] on the existence and properties of solutions of second-order variational inequalities with L 1 -right-hand sides and sufficiently general constraints. Note that in [20][21][22][23] right-hand sides to the investigated variational inequalities and equations depend on independent variables only, and belong to the class L 1 .…”

Section: Introductionmentioning

confidence: 99%

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Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Gorban

2017

Open Mathematics

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Abstract:In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L 1 -right-hand sides in a bounded domain of R n .n > 2/. This class is described by the presence of a set of exponents q 1 ; : : : ; q n and a set of weighted functions 1 ; : : : ; n in growth and coercitivity conditions on coefficients of the equations. The exponents q i characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions i characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to investigate the existence of entropy solutions of the problem under consideration.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Gorban

2017

Open Mathematics

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“…Now right-hand sides to the given equations depend on independent variables and unknown function. In our case we have no opportunity to use the results [11]- [13] directly. We follow a general approach for proving the main result of this work (theorem 1).…”

mentioning

confidence: 99%

“…Observe that the proof of this theorem is based on use of some results of [11]- [13] on the existence and properties of solutions of second-order variational inequalities with L 1 -right-hand sides and sufficiently general constraints. Note that in [11]- [14] right-hand sides to the investigated variational inequalities and equations depend on independent variables only, and belong to the class L 1 . The present paper is devoted to the Dirichlet problem for the same class of the nonlinear elliptic second-order equations in divergence form with degenerate anisotropic coefficients as in [14].…”

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confidence: 99%

On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Gorban

2017

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. On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations, Mat. Stud. 47 (2017), 59-70.In the present paper we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L 1 -right-hand sides in a bounded domain of R n (n 2). This class is described by the presence of a set of exponents q 1 , . . . , q n and a set of weighted functions ν 1 , . . . , ν n in growth and coercitivity conditions on coefficients of the equations. The exponents q i characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions ν i characterize degeneration or singularity of the coefficients with respect to independent variables. Our aim is to study the uniqueness of entropy solution of the problem under consideration.

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On the Boundedness of Solutions of Degenerate Anisotropic Elliptic Variational Inequalities

Gorban

Kovalevsky

2013

Results. Math.

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On $ T$-solutions of degenerate anisotropic elliptic variational inequalities with $ L^1$-data

Cited by 6 publications

References 30 publications

Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

On uniqueness of entropy solutions for nonlinear elliptic degenerate anisotropic equations

On the Boundedness of Solutions of Degenerate Anisotropic Elliptic Variational Inequalities

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