## Global Hölder regularity for discontinuous elliptic equations in the plane

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- by Sofia Giuffrè
- Proc. Amer. Math. Soc.
**132**(2004), 1333-1344 - DOI: https://doi.org/10.1090/S0002-9939-03-07348-9
- Published electronically: December 22, 2003
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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{equation*} \begin {array}{ll} u= g(x) &\ \rm on \: \partial \Omega \end{array} \end{equation*} where $g(x) \in W^{2- \frac {1}{r}, r}(\partial \Omega )$, $r>2$, or with the following normal derivative boundary conditions: \begin{equation*} \begin {array}{lclr} \displaystyle \frac {\partial u}{\partial n} = h( x) &\ \rm or &\ \displaystyle \frac {\partial u}{\partial n} + \sigma u = h( x) &\ \rm on \: \partial \Omega \end{array} \end{equation*} 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 $\partial \Omega$.## References

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## Bibliographic 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
- Received by editor(s): April 1, 2002
- Published electronically: December 22, 2003
- Communicated by: David S. Tartakoff
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2053337