# Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 768-786
- ISSN: 2391-5455

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topYuliya Gorban. "Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations." Open Mathematics 15.1 (2017): 768-786. <http://eudml.org/doc/288533>.

@article{YuliyaGorban2017,

abstract = {In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of ℝn(n ⩾ 2) . This class is described by the presence of a set of exponents q1,…, qn and a set of weighted functions ν1,…, νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi 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.},

author = {Yuliya Gorban},

journal = {Open Mathematics},

keywords = {Nonlinear elliptic degenerate anisotropic second-order equations; L1-data; Dirichlet problem; Existence of entropy solutions},

language = {eng},

number = {1},

pages = {768-786},

title = {Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations},

url = {http://eudml.org/doc/288533},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Yuliya Gorban

TI - Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 768

EP - 786

AB - In the present article we deal with the Dirichlet problem for a class of degenerate anisotropic elliptic second-order equations with L1-right-hand sides in a bounded domain of ℝn(n ⩾ 2) . This class is described by the presence of a set of exponents q1,…, qn and a set of weighted functions ν1,…, νn in growth and coercitivity conditions on coefficients of the equations. The exponents qi characterize the rates of growth of the coefficients with respect to the corresponding derivatives of unknown function, and the functions νi 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.

LA - eng

KW - Nonlinear elliptic degenerate anisotropic second-order equations; L1-data; Dirichlet problem; Existence of entropy solutions

UR - http://eudml.org/doc/288533

ER -

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