Local boundedness of weak solutions to elliptic equations with $ p, q- $growth-Reference-Cited by-同舟云学术

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

Published:2023 Issue:3 Volume:5 Page:1-28
ISSN:2640-3501
Container-title:Mathematics in Engineering
language:
Short-container-title:MINE

Author:

Cupini Giovanni¹,Marcellini Paolo²,Mascolo Elvira²

Affiliation:

1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 - Bologna, Italy

2. Dipartimento di Matematica e Informatica "U. Dini", Università di Firenze, Viale Morgagni 67/A, 50134 - Firenze, Italy

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

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