Local boundedness of weak solutions to elliptic equations with p,q−growth

This article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the <italic>local boundedness</italic> of weak solutions to a class of nonlinea...

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Bibliographic Details
Main Authors: Giovanni Cupini, Paolo Marcellini, Elvira Mascolo
Format: Article
Language:English
Published: AIMS Press 2023-09-01
Series:Mathematics in Engineering
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/mine.2023065?viewType=HTML
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Summary:This article is dedicated to Giuseppe Mingione for his $ 50^{th} $ birthday, a leading expert in the regularity theory and in particular in the subject of this manuscript. In this paper we give conditions for the <italic>local boundedness</italic> of weak solutions to a class of nonlinear elliptic partial differential equations in divergence form of the type considered below in (1.1), under $ p, q- $growth assumptions. The novelties with respect to the mathematical literature on this topic are the general growth conditions and the explicit dependence of the differential equation on $ u $, other than on its gradient $ Du $ and on the $ x $ variable.
ISSN:2640-3501