Partial regularity result for non-autonomous elliptic systems with general growth

Teresa Isernia; Chiara Leone; Anna Verde

doi:10.3934/cpaa.2021160

Article Contents

2021, Volume 20, Issue 12: 4271-4305. Doi: 10.3934/cpaa.2021160

This issue Previous Article Periodic solutions for a class of second-order differential delay equations Next Article Local well-posedness for the Zakharov system in dimension

$ d = 2, 3 $

Partial regularity result for non-autonomous elliptic systems with general growth

1.
Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, via brecce bianche 12, 60131 Ancona, Italy
2.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli Federico II, via Cinthia, 80126 Napoli, Italy

^* Corresponding author
^* Corresponding author

Received: January 31, 2021

Revised: March 31, 2021

Early access: September 2021

Published: December 2021

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Abstract

In this paper we prove a partial Hölder regularity result for weak solutions $ u:\Omega\to \mathbb{R}^N $, $ N\geq 2 $, to non-autonomous elliptic systems with general growth of the type:

$ \begin{equation*} -{\rm{div}} a(x, u, Du) = b(x, u, Du) \quad \;{\rm{ in }}\; \Omega. \end{equation*} $

The crucial point is that the operator $ a $ satisfies very weak regularity properties and a general growth, while the inhomogeneity $ b $ has a controllable growth.

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Mathematics Subject Classification: Primary: 35J47, 35B65; Secondary: 46E30.

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