Pointwise estimates for \(G\Gamma\)-functions and applications. (English) Zbl 1413.35161

The authors obtain new regularity results in small Lebesgue spaces for the weak or the very weak solution of a linear elliptic equation. The contribution is interesting because the authors improve previous results obtained in the classical Lebesgue spaces. Some of the obtained results have been derived using borderline Sobolev embeddings associated to the Grand Lebesgue spaces. Moreover, another goal is to provide some new Sobolev inclusions using the Generalized Gamma spaces and generalizing the Fusco-Lions-Sbordone results.


35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems