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.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 $n=2$.
In questo lavoro studiamo la regolarità fino alla frontiera di soluzioni di un problema di Dirichlet non omogeneo per sistemi ellittici discontinui del secondo ordine con non linearità $q>1$ e con andamenti naturali. Scopo del lavoro è illustrare che le soluzioni del suddetto problema sono sempre globalmente hölderiane nel caso di dimensione $n=q$ senza alcun tipo di condizione di regolarità sui coefficienti. Come conseguenza di questo risultato, gli insiemi singolari $\Omega_{0}\subset \Omega$, $\Sigma_{0}\subset\partial\Omega$ sono sempre vuoti per $n=q$. Inoltre dimostriamo che anche per $1$, ma $q$ sufficientemente vicino a 2, le soluzioni sono globalmente hölderiane per $n=2$. 
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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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