Basics for P.D.E. Systems

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


The main object in this chapter is the stress-energy tensor, which is an algebraic fact implying several useful identities like the (weak) monotonicity formula, Gui’s Hamiltonian identities, and Pohozaev’ identities, for all solutions and all potentials W ≥ 0. Modica’s inequality holds in the scalar case and implies a strong monotonicity formula, but is not generally valid in the vector case. The triple junction on the plane is also introduced.


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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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