Main results on well-posedness

Abstract

The starting point of this chapter is the model problem derived in the previous chapter. Our goal is to specify conditions under which this problem is well-posed. Two important results are presented: the Lax–Milgram lemma and the more fundamental Banach–Nečas–Babuška theorem. The former provides a sufficient condition for well-posedness, whereas the latter, relying on slightly more sophisticated assumptions, provides necessary and sufficient conditions.