Calculus of Variations and Geometric Measure Theory

A. P. Migliorini

Everywhere regularity for a class of elliptic systems with $p$, $q$ growth conditions

created on 18 Dec 2001


Published Paper

Inserted: 18 dec 2001

Journal: Rend. Ist. Mat. Trieste
Volume: XXXI
Pages: 203-234
Year: 1999




We shall prove everywhere regularity for weak solutions of elliptic systems of the form $$\sum\frac{\partial}{\partial x{i}}a(x,
)u{\alpha}{x{i}}=0$$ under general $p$, $q$ growth conditions and in particular for minimizers for a class of variational integrals whose models is $$I(u)=\int{\Omega}a(x)\left( 1+
{2}\right){\frac{\alpha(x)}{2}}dx $$ \end{document}

Keywords: regularity, Non standard growth conditions