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The Cut-Off Lemma and a Maximum Principle

  • Nicholas D. Alikakos
  • Giorgio Fusco
  • Panayotis Smyrnelis
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 91)

Abstract

In this chapter we establish a maximum principle type result that provides pointwise control on minimal solutions. In contrast to the usual maximum principle, it does not hold for solutions in general, not even for local minimizers in the scalar case. We obtain it as a corollary of a replacement lemma modeled after Lemmas  2.4 and  2.5.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Nicholas D. Alikakos
    • 1
  • Giorgio Fusco
    • 2
  • Panayotis Smyrnelis
    • 3
  1. 1.Department of MathematicsNational and Kapodistrian UniversityAthensGreece
  2. 2.Department of MathematicsUniversity of L’AquilaCoppitoItaly
  3. 3.Center for Mathematical ModelingUniversity of ChileSantiagoChile

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