A priori estimates for solutions of the first initial boundary-value problem for systems of fully nonlinear partial differential equations

We prove a priori estimates for a solution of the first initial boundary-value problem for a system of fully nonlinear partial differential equations (PDE) in a bounded domain. In the proof, we reduce the initial boundary-value problem to a problem on a manifold without boundary and then reduce the resulting system on the manifold to a scalar equation on the total space of the corresponding bundle over the manifold. St. Petersburg Architecture Building University, St. Petersburg. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 338–363, March, 1997.