Differential and Integral Equations

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

Alberto Fiorenza, Maria Rosaria Formica, and Jean Michel Rakotoson

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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

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

First available in Project Euclid: 1 September 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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