On a coupled problem between the plate equation and the membrane equation on polygons
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
The article studies a second-order linear differential operator of the type
This article surveys results on the global surjectivity of linear partial differential operators with constant coefficients on the space of real analytic functions. Some new results are also included.