arXiv subjects

A. C. Faliagas

Publications and source records attributed to A. C. Faliagas.

2 recordsLinked to original sources

arXiv2015

Stability Criteria for Multiphase Partitioning Problems with Volume Constraints

We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign of the principal eigenvalue of the Jacobi operator. We thus derive certain stability criteria, and in particular we recapture the Sternberg-Zumbrun result on the instability of the disconnected phases in the more general setting of several phases.

math.AP↗

arXiv2013

On the equivalence of Euler-Lagrange and Noether equations

We prove that on the condition of non-trivial solutions, the Euler-Lagrange and Noether equations are equivalent for the variational problem of nonlinear Poisson equation and a class of more general Lagrangians, including position independent and of p-Laplacian type. As applications we prove certain propositions concerning the nonlinear Poisson equation and its generalisations, the equivalence of admissible and inner variations and discuss the inverse problem of determining the Lagrangian from conservation or symmetry laws.

math.AP↗