Recent developments in problems with nonstandard growth and nonuniform ellipticity -
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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 …

Modular density of smooth functions in inhomogeneous and fully anisotropic Musielak–Orlicz–Sobolev
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A sharp pointwise differential inequality for vectorial second-order partial differential
operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order …

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 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 investigate solutions to nonlinear elliptic Dirichlet problems of the type {− div A (x, u,∇
u)= μ in Ω, u= 0 on∂ Ω, where Ω is a bounded Lipschitz domain in R n and A (x, z, ξ) is a …

We establish pointwise estimates expressed in terms of a nonlinear potential of a
generalized Wolff type for $ A $-superharmonic functions with nonlinear operator …

The purpose of this work is to prove the existence and uniqueness of a class of nonlinear
unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non …