The purpose of this article is to present existence theorems for various equilibrium boundary-
value problems of nonlinear elasticity in one, two and three dimensions under realistic …

In their pioneering work on quasilinear elliptic equations, Ladyzhenskaya and Ural'tseva
[a],[I21 introduced so-called natural conditions for the structure of an elliptic operator in …

This paper gives a Sobolev-type embedding theorem for the generalized Lebesgue–
Sobolev space Wk, p (x)(Ω), where Ω is an open domain in RN (N≥ 2) with cone property …

For/2 a domain in [R n and f:/2-+[R~, f=(fl...., fn) a map** of Sobolev class W~ P (/2,~), 1=<
p< 0% we denote by Df (x):~ R n the differential and by J (x, f)= det Df (x) the Jacobian of f …

Homogenization theory describes the macroscopic properties of structures with fine
microstructure. Its applications are diverse and include optimal design and the study of …

Variational boundary value problems for quasilinear elliptic systems in divergence form are
studied in the case where the nonlinearities are nonpolynomial. Monotonicity methods are …

Hypersingular integrals arise as constructions inverse to potential-type operators and are
realized by the methods of regularization and finite differences. This volume develops these …

Homogenization is a method for modeling processes in microinhomogeneous media, which
are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other …

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

In this paper we are concerned with a new class of anisotropic quasilinear elliptic equations
with a power-like variable reaction term. One of the main features of our work is that the …