Abstract
This chapter provides a comprehensive presentation of regularity theorems and maximum principles that are essential for the subsequent study of nonlinear elliptic boundary value problems. In addition to the presentation of fundamental results, the chapter offers, to a large extent, a novel approach with clarification of tedious arguments and simplification of proofs. The first section of this chapter treats two major topics related to weak solutions of nonlinear elliptic problems: boundedness and regularity. The second section has as its objective to report on maximum and comparison principles. It comprises two parts: local results and strong maximum principles. Comments and related references are given in a remarks section.
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