Maximum Principles in Sobolev Spaces

InMaximum principle this chapter we prove various maximum principles for second order, elliptic differential operators with discontinuous coefficients such as the weak and strong maximum principles (Theorems 8.1 and 8.9) and the Hopf boundary point lemma (Lemma 8.8) in the framework of \(L^{p}\) Sobolev spacesSobolev space that will play an important role in the proof of uniqueness theorems for the Dirichlet problem in Part IV.