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Regularity Theorems and Maximum Principles

In: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dumitru Motreanu & Viorica Venera Motreanu & Nikolaos Papageorgiou, 2014. "Regularity Theorems and Maximum Principles," Springer Books, in: Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, edition 127, chapter 0, pages 201-222, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-9323-5_8
    DOI: 10.1007/978-1-4614-9323-5_8
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