Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent

Abstract

Abstract. The aim of this paper is to study the existence of solutions in the sense of distributions for a strongly nonlinear elliptic problem where the second term of the equation f is in W −1, − → p ′ ( · ) (Ω) which is the dual space of the anisotropic Sobolev(Ω) and later f will be in L 1 (Ω).

Existence of renormalized solutions to elliptic equation in Musielak–Orlicz space

“…For the recent existence results for elliptic problems we refer to [1,2,5,6,14,15,29,24,25,27,29,30]. In [15,27,30] isotropic, separable and reflexive Musielak-Orlicz spaces are employed, [5] concerns anisotropic variable exponent spaces, [14] studies separable, but not reflexive Musielak-Orlicz spaces, while [29] anisotropic, but separable and reflexive Orlicz spaces. Renormalized solutions to elliptic problems in Orlicz spaces are explored in [1,2,6], while in Musielak-Orlicz spaces in [24,25].…”

“…The existence theory for problems in this setting arising from fluids mechanics is developed from various points of view [20, ?, 22, 43]. For the recent existence results for elliptic problems we refer to [1,2,5,6,14,15,29,24,25,27,29,30]. In [15,27,30] isotropic, separable and reflexive Musielak-Orlicz spaces are employed, [5] concerns anisotropic variable exponent spaces, [14] studies separable, but not reflexive Musielak-Orlicz spaces, while [29] anisotropic, but separable and reflexive Orlicz spaces.…”

Renormalized solutions for a p(·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponent

“…In this work, we extend the approach developed in [3,4,8] to the case of maximal monotone graph or and Radon diffuse measure data. Elliptic problems with variable exponent has been extensively studied in recent years (see [3,4,5,6,7,9,18,19,20,22,23]) and the references therein. The interest of studying problems with variable exponent is due to the fact they can model phenomena which arise in mathematical physics such that elastic mechanics, electro-rheological fluid dynamics and image processing (see [20,23]).…”

Nonlinear Degenerate Anisotropic Elliptic Equations with Variable Exponents and L¹ Data

“…Eq., 33 (2020), pp. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Carathéodory functions such that for almost every x in Ω and for every (σ,ξ) ∈ R×R N the following assumptions are satisfied for all i = 1,..., N…”