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An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem

100%
Wiśniewski D., Bodzioch M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
2
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Existence of entropy solutions for nonlinear elliptic degenerate anisotropic equations

100%
Gorban Y.
Open Mathematics
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2017
|
tom 15
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nr 1
768-786
EN
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.
3
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Comments on behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities

84%
Bodzioch M., Wiśniewski D., Żyjewski K.
Open Mathematics
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2017
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tom 15
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nr 1
667-678
EN
We have investigated the behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities in bounded and unbounded domains. We found exponents of the solution’s decreasing rate near the boundary singularities.
4
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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

84%
Ammar K.
Open Mathematics
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2010
|
tom 8
|
nr 3
548-568
EN
The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.
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