Geodesic
Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 519-524

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In this paper we deal with the Hölder regularity up to the boundary of the solutions to a nonhomogeneous Dirichlet problem for second order discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth. The aim of the paper is to clarify that the solutions of the above problem are always global Hölder continuous in the case of the dimension $n=q$ without any kind of regularity assumptions on the coefficients. As a consequence of this sharp result, the singular sets are always empty for $n=q$.Moreover we show that also for $1$, but $q$ close enough to 2, the solutions are global Hölder continuous for $n=2$. 
Giuffrè, Sofia; Idone, Giovanna. Global regularity for solutions to Dirichlet problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 519-524. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a14/
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     title = {Global regularity for solutions to {Dirichlet} problem for discontinuous elliptic systems with nonlinearity $q>1$ and with natural growth},
     journal = {Bollettino della Unione matematica italiana},
     pages = {519--524},
     year = {2005},
     volume = {Ser. 8, 8B},
     number = {2},
     zbl = {1150.35028},
     mrnumber = {MR2149398},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a14/}
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