Grand Sobolev spaces and their applications in geometric function theory and PDEs

A note on the continuity of minors in grand Lebesgue spaces

“…Grand Lebesgue spaces have been thoroughly studied by many different authors. We refer the interested reader to the reviews given in articles [9,12,27] and [6, §7.2]. However, we now state some basic properties of these spaces which will be useful for the results that follow.…”

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

“…If θ 1 < θ 2 then for 0 < ε < p − 1 the embeddings: hold. Note that the information about properties and applications of the grand Lebesgue spaces can be found in [11,13,26,33,35,36].…”

Regularity of the inverse mapping in Banach function spaces

“…At the same time, concerning continuum mechanics, the study of function spaces, different from the ones of smooth or Sobolev mappings, is of great interest. In particular, there are advantages in using Sobolev–Orlicz spaces for nonlinear elasticity [4], Lorentz spaces for the Shrödinger equation [6] and for the p ‐Laplace system [1], grand Sobolev spaces for p ‐harmonic operators [10, 18]. Thoroughly studied, has been the question of the regularity of derivatives of the inverse mapping.…”