## Differential and Integral Equations

### Pointwise estimates for $G\Gamma$-functions and applications

#### Abstract

Some regularity results in small Lebesgue spaces for the weak or the very weak solution of the linear equation $-\Delta u = f$ are given, improving all the previous results obtained in the usual Lebesgue spaces. Some of our results have been derived using borderline Sobolev embeddings related to the Grand Lebesgue spaces. So, we provide new Sobolev inclusions using the Generalized Gamma spaces and generalizing the Fusco-Lions-Sbordone results.

#### Article information

Source
Differential Integral Equations, Volume 30, Number 11/12 (2017), 809-824.

Dates
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1504231274

Mathematical Reviews number (MathSciNet)
MR3693986

Zentralblatt MATH identifier
06819579

Subjects
Primary: 35J25, 35B65, 46E30, 46E35

#### Citation

Fiorenza, Alberto; Formica, Maria Rosaria; Rakotoson, Jean Michel. Pointwise estimates for $G\Gamma$-functions and applications. Differential Integral Equations 30 (2017), no. 11/12, 809--824. https://projecteuclid.org/euclid.die/1504231274