On the regularity up to the boundary for certain nonlinear elliptic systems

Luigi C.  Berselli; Carlo R.  Grisanti

doi:10.3934/dcdss.2016.9.53

Article Contents

2016, Volume 9, Issue 1: 53-71. Doi: 10.3934/dcdss.2016.9.53

This issue Previous Article Elliptic boundary value problems in spaces of continuous functions Next Article On the concentration of entropy for scalar conservation laws

On the regularity up to the boundary for certain nonlinear elliptic systems

Luigi C. Berselli^1, and
Carlo R. Grisanti^1,

1.
Dipartimento di Matematica, Via F. Buonarroti 1/c, Pisa, I-56127

Received: September 2014

Revised: February 2015

Published: February 2016

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Abstract

We consider a class of nonlinear elliptic systems and we prove regularity up to the boundary for second order derivatives. In the proof we trace carefully the dependence on the various parameters of the problem, in order to establish, in a further work, results for more general systems.

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Mathematics Subject Classification: Primary: 35J25; Secondary: 35B65, 35J70.

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