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Elliptic Systems of Phase Transition Type pp 87–109Cite as

Birkhäuser

Basics for P.D.E. Systems

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 91))

Abstract

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

  1. Department of Mathematics, National and Kapodistrian University, Athens, Greece

    Nicholas D. Alikakos

  2. Department of Mathematics, University of L’Aquila, Coppito, Italy

    Giorgio Fusco

  3. Center for Mathematical Modeling, University of Chile, Santiago, Chile

    Panayotis Smyrnelis

Authors
  1. Nicholas D. Alikakos
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  2. Giorgio Fusco
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  3. Panayotis Smyrnelis
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Alikakos, N.D., Fusco, G., Smyrnelis, P. (2018). Basics for P.D.E. Systems. In: Elliptic Systems of Phase Transition Type. Progress in Nonlinear Differential Equations and Their Applications, vol 91. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-90572-3_3

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