Generalized solutions for nonlinear elliptic equations.
Existence result for nonlinear parabolic problems with L¹-data
We study the existence of solutions of the nonlinear parabolic problem in ]0,T[ × Ω, on ]0,T[ × ∂Ω, u(0,·) = u₀ in Ω, with initial data in L¹. We use a time discretization of the continuous problem by the Euler forward scheme.
Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and -data
In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic -Laplacian problem with Dirichlet-type boundary conditions and data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.
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