In this chapter we will discuss the main objects in general potential theories; that is, subequation constraint sets and their subharmonics. Both classical and viscosity formulations will be discussed as well as the relations between the two notions. A few representative potential theories will be presented; namely classical subharmonics, convex and semiconvex functions.

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General Potential Theories

  • Kevin R. Payne,
  • Davide Francesco Redaelli

摘要

In this chapter we will discuss the main objects in general potential theories; that is, subequation constraint sets and their subharmonics. Both classical and viscosity formulations will be discussed as well as the relations between the two notions. A few representative potential theories will be presented; namely classical subharmonics, convex and semiconvex functions.