On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients

Sofia Giuffrè; Giovanna Idone

doi:10.3934/dcds.2011.31.1347

Article Contents

2011, Volume 31, Issue 4: 1347-1363. Doi: 10.3934/dcds.2011.31.1347

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On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients

Sofia Giuffrè^1, and
Giovanna Idone^1,

1.
D.I.M.E.T., Department of Computer Science, Mathematics, Electronics and Transportations, “Mediterranea” University of Reggio Calabria, 89060 Reggio Calabria

Received: February 28, 2010

Revised: August 31, 2010

Published: September 2011

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Abstract

Global Hölder regularity of the gradient in Morrey spaces is established for planar elliptic discontinuous equations, estimating in an explicit way the Hölder exponent in terms of the eigenvalues of the operator. The result is proved for Dirichlet or normal derivative problems and for nonlinear operators.

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Mathematics Subject Classification: Primary: 35J25; Secondary: 35J65.

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References

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