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 the density of smooth functions in the modular topology in Musielak–Orlicz–
Sobolev spaces essentially extending the results of Gossez [17] obtained in the Orlicz …

We prove Harnack's inequality for local (quasi) minimizers in generalized Orlicz spaces
without polynomial growth or coercivity conditions. As a consequence, we obtain the local …

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∈ …

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 investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general
anisotropic N-function, which is not necessarily of power-type and need not satisfy the Δ _2 …

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 study nonlinear measure data elliptic problems involving the operator of generalized
Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of …

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