The maximum principle for semicontinuous functions

Michael G. Crandall, Hitoshi Ishii

研究成果: Article査読

71 被引用数 (Scopus)

抄録

The result of calculus which states that at a maximum of a twice differentiable function the gradient vanishes and the matrix of second derivatives is nonpositive plays a significant role in the theory of elliptic and parabolic differential equations of second order, where it is used to establish many results for solutions of these equations. The theory of viscosity solutions of fully nonlinear degenerate elliptic and parabolic equations, which admits nondifferentiable functions as solutions of these equations, is now recognized to depend on a "maximum principle" for semicontinuous functions, which replaces the calculus result mentioned above. This work contains a more general statement of this form together with a simpler proof than were available heretofore.

本文言語English
ページ(範囲)1001-1014
ページ数14
ジャーナルDifferential and Integral Equations
3
6
出版ステータスPublished - 1990
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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