Analytic semigroups generated on Hölder spaces by second order elliptic systems under Dirichlet boundary conditions (Q1070104)

The authors study the problem of the generation of analytic semigroups on Hölder spaces by the following elliptic operator, under Dirichlet boundary conditions, \[ Eu=\sum^{n}_{i,j=1}A_{ij}\Delta_{ij}u(x)+\sum^{n}_{j=1}B_ j\Delta_ ju(x)+Cu(x);\quad x\in \Omega \subset \subset R^ n;\quad u: \Omega \to C^ M \] where the coefficients \(A_{ij}(x)\), \(B_ j(x)\), C(x) are \(N\times N\) complex valued matrices.