Everywhere regularity for a class of elliptic systems with p, q growth conditions
Anna Paola Migliorini · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 1999
We shall prove everywhere regularity for weak solutions of elliptic systems of the form \\[ \\sum\\frac{\\partial}{\\partial x_{i}}a\\left(x,\\mid Du\\mid\\right)u_{x_{i}}^{\\alpha}=0 \\] under general p, q growth conditions and in particular for minimizers of a class of variational integrals, both degenerate and non degenerate ones, whose models are \\[ \\begin{array}{c} I_{1}\\left(u\\right)\\quad=\\quad\\int_{\\Omega}a\\left(x\\right)\\mid Du\\mid^{b\\left(x\\right)}dx,\\\\ I_{2}\\left(u\\right)\\quad=\\quad\\int_{\\Omega}a\\left(x\\right)\\left(1+\\mid Du\\mid^{2}\\right)^{\\frac{b\\left(x\\right)}{2}}dx. \\end{array} \\]