Entropy solution for nonlinear elliptic problem involving variable exponent and Fourier type boundary condition

Multivalued anisotropic problem with Fourier boundary condition involving diffuse Radon measure data and variable exponents

“…In particular, as the domain of β is bounded, this equivalent formulation is very useful for the proof of uniqueness of solution to problem (1.1). We reason as in [25] to get the following results. (Ω) such that ϕ ∈ dom β and for any k > 0…”

“…Note that the space in which we work is the anisotropic Sobolev space W In the classical Lebesgue and Sobolev spaces with constant exponent, many authors have studied problems with a maximal monotone graph and measure data (see [3,4,5,11,13,19]). These problems have been extended to the Sobolev spaces with variable exponent in the context of isotropic operators (see [25,27]). In this paper, we extend the study of problems with maximal monotone graph and measure data to the Sobolev spaces with variable exponents in the context of anisotropic operators.…”

Renormalized solutions to a reaction-diffusion system applied to image denoising

“…The definition of renormalized solutions. Recall the following space introduced in [3,23]. Denote T K the truncation function at height K ≥ 0:…”

Nonlinear elliptic p(u)− Laplacian problem with Fourier boundary condition

“…studied in [15] by Nyanquini and Ouaro. The authors used an auxiliary result due to Le (see [16], Theorem 3.1) to prove the existence of the weak solution when f ∈ L ∞ (Ω), g ∈ L ∞ (∂Ω) and by approximation methods they obtained the entropy solution when f ∈ L 1 (Ω), g ∈ L 1 (∂Ω).…”

“…We were inspired by the work of Ouaro and Tchousso (see [15]), where the authors defined for the first time a new space by taking into account the boundary.…”