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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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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