Anisotropic and inhomogeneous spaces, which are at the core of the present study, may
appear exotic at first. However, the reader should abandon this impression once they realize …

Abstract The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev,
and double-phase spaces. They inherit technical difficulties resulting from general growth …

We prove existence of renormalized solutions to general nonlinear elliptic equation in
Musielak–Orlicz space avoiding growth restrictions. Namely, we consider− div A (x,∇ u)= f∈ …

Modular density of smooth functions in inhomogeneous and fully anisotropic Musielak–Orlicz–Sobolev
spaces - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books …

In this paper we mainly prove the existence and uniqueness of entropy solutions and the
uniqueness of renormalized solutions to the general nonlinear elliptic equations in Musielak …

We study a general class of nonlinear elliptic problems associated with the differential
inclusion β (x, u)− div (a (x,∇ u)+ F (u))∋ f, where f∈ L1 (Ω). The vector field a (⋅,⋅) is …

We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a
non-autonomous variational problem of a general structure, where the integrand is assumed …

We study a general nonlinear parabolic equation on a Lipschitz bounded domain in RN,{∂
tu− div A (t, x,∇ u)= f (t, x) in Ω T, u (t, x)= 0 on (0, T)×∂ Ω, u (0, x)= u 0 (x) in Ω, with f∈ L∞(Ω …

We prove existence and uniqueness of renormalized solutions to general nonlinear
parabolic equation in Musielak–Orlicz space avoiding growth restrictions. Namely, we …

We will present the proof of existence of renormalized solutions to a nonlinear parabolic
problem∂ tu− div a (⋅, D u)= f with right-hand side f and initial data u 0 in L 1. The growth …