ON THE BOUNDARY CONDITIONS FOR PARTIAL DIFFERENTIAL EQUATIONS

Let Ω be a bounded and closed region in Rwith a smooth boundary S. It is proved that for any given integers k and m, 0 ≤ k ≤ m, there exists a class of partial differential operators of order m such that the Csolution to the following boundary value problem exists uniquely. Here P is the differential operator and f, φo, …, φk-1 are arbitrarily sufficient-smooth functions. Especially, when k=0, there exists only one Csolution to the equation Pu=f.