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Global Hölder regularity for discontinuous elliptic equations in the plane


Author: Sofia Giuffrè
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1333-1344
MSC (2000): Primary 35J25; Secondary 35J65
DOI: https://doi.org/10.1090/S0002-9939-03-07348-9
Published electronically: December 22, 2003
MathSciNet review: 2053337
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Abstract: $C^{1, \mu}$-regularity up to the boundary is proved for solutions of boundary value problems for elliptic equations with discontinuous coefficients in the plane.

In particular, we deal with the Dirichlet boundary condition

\begin{displaymath}\begin{array}{ll} u= g(x) & \rm on \: \partial\Omega \end{array}\end{displaymath}

where $g(x) \in W^{2- \frac{1}{r}, r}(\partial \Omega)$, $r>2$, or with the following normal derivative boundary conditions:

\begin{displaymath}\begin{array}{lclr} \displaystyle \frac{\partial u}{\partial ... ...al n} + \sigma u = h( x) & \rm on \: \partial\Omega \end{array}\end{displaymath}

where $h(x) \in W^{1- \frac{1}{r}, r}(\partial \Omega)$, $r>2$, $\sigma >0$ and $n$ is the unit outward normal to the boundary $\partial \Omega$.


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Additional Information

Sofia Giuffrè
Affiliation: D.I.M.E.T., Faculty of Engineering, University of Reggio Calabria, Via Graziella, Località Feo di Vito, 89100 Reggio Calabria, Italy
Email: giuffre@ing.unirc.it

DOI: https://doi.org/10.1090/S0002-9939-03-07348-9
Keywords: Regularity up to the boundary, elliptic equations, boundary value problems
Received by editor(s): April 1, 2002
Published electronically: December 22, 2003
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2003 American Mathematical Society

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