A remark on non variational basic parabolic systems of second order of Campanato type. (English) Zbl 0823.35093

Amato, R.

Rend. Semin. Mat., Torino 51, No. 2, 105-108 (1993).

Summary: We consider the non-variational basic operator \(a(H(u))- {{\partial u} \over {\partial t}}\) where \(a(\xi)\) is a vector in \(\mathbb{R}^ N\), \(N\geq 1\), which is continuous in \(\xi\) and satisfies the condition (A) first introduced by S. Campanato and used to solve the Cauchy-Dirichlet problem. We show that also for a particular Cauchy-Newman problem condition (A) is effective.

MSC:

35K60

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations

Keywords:

non variational basic parabolic systems; systems of Campanato type