The general theorem of Necas admits a simple proof

Abstract

In this note, we shall study a new, short proof of the general theorem of Necas about the solvability of linear partial differential equations in the Banach space setting. The complexity of this proof does not seem to be greater than that of the Lax-Milgram theorem, and since the theorem of Necas is strictly stronger than the Lax-Milgram theorem, the author hopes that his new proof will help the theorem of Necas to gain prominence in PDE and functional analysis lectures.