On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces

The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

“…For that, we borrow ideas from Evans [13], Demangel-Hebey [12] and Koznikova L. M. [21,22]. Let δ > 0 be given.…”

“…For more results we refer the reader to the work [16]. We mention [17][18][19], for the Sobolev space with variable exponent, and [20][21][22][23][24][25][26] for the classical anisotropic space. The oddity of our present paper is to continue in this direction and to show the existence and uniqueness of entropy solution for equations (P ) governed with growth and described by an N-uplet of N-functions satisfying the ∆ 2 -condition, within the fulfilling of anisotropic Orlicz spaces.…”

On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space

“…; N; b i ðx; u; ∇uÞ : Ω 3 R 3 R N → R are the Carath eodory functions that do not satisfy any sign condition and the growth described by the vector N-function B(θ). After that, Kozhevnikova in [28] established the existence of entropy solutions in an unbounded domain to the following problem:…”

On solutions of anisotropic elliptic equations with variable exponent and measure data

“…Questions about the existence and uniqueness of renormalized and entropy solutions of the Dirichlet problem for elliptic equations of the second order with non-power nonlinearities and µ ∈ L 1 (Ω) (Ω is a bounded domain) in Sobolev-Orlicz spaces were studied in [7], [8], [9]. Theorems on the existence and uniqueness of entropy solutions of the Dirichlet problem in arbitrary domains for a class of anisotropic elliptic equations with non-power nonlinearities in Sobolev-Orlicz spaces were proved by the author in [10], [11]. Since then, a lot of articles have been devoted to these issues, see the surveys [12], [13].…”