Regularity Theorems and Maximum Principles

Dumitru Motreanu, Viorica Venera Motreanu and Nikolaos Papageorgiou
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Dumitru Motreanu: University of Perpignan, Department of Mathematics
Viorica Venera Motreanu: Ben-Gurion University of the Negev, Department of Mathematics
Nikolaos Papageorgiou: National Technical University, Department of Mathematics

Chapter Chapter 8 in Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 2014, pp 201-222 from Springer

Abstract: 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.

Keywords: Weak Solution; Maximum Principle; Comparison Principle; Regularity Result; Strong Maximum Principle (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-9323-5_8

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DOI: 10.1007/978-1-4614-9323-5_8

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