Czechoslovak Mathematical Journal, Vol. 58, No. 1, pp. 113-129, 2008

# A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

## Luisa Fattorusso

L. Fattorusso, DIMET, Facolta di Ingegneria Universita "Mediterranea" degli Studi di Reggio Calabria, Via Graziella (Loc. Feo Di Vito), Reggio Calabria, Italy, e-mail: luisa.fattorusso@unirc.it

Abstract: Let $\Omega$ be a bounded open subset of $\Bbb R^n$, $n>2$. In $\Omega$ we deduce the global differentiability result
u \in H^2(\Omega, \Bbb R^N)
for the solutions $u \in H^1(\Omega, \Bbb R^n)$ of the Dirichlet problem
\gather u-g \in H^1_0(\Omega, \Bbb R^N),
-\sum_iD_ia^i(x,u,Du)=B_0(x,u,Du)
with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.

Keywords: global differentiability of weak solutions, elliptic problems, controlled growth, nonlinearity with $q=2$

Classification (MSC 2000): 35J60, 35D10, 58B10

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).