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Some monotonicity results for general systems of nonlinear elliptic PDEs. (English) Zbl 1342.35101

Monotonicity properties of minimizers and stable critical points of a general energy functional on domains of Euclidean spaces are studied in the paper. It is well organized, interesting and presented in seven sections.
After a detailed introduction, in Section 2, it is shown that, under suitable assumptions, the notion of \(\{e_n,e_{n+1}\}\)-stability is equivalent to the notion of classical stability. In Section 3, a local analysis is given and, in Section 4, the energy of the perturbation at infinity is estimated. The main results are Theorems 1.5 and 1.10 proved in Sections 5 and 6, respectively. In Section 7, two applications are given. The first one is to a system in the analysis of phase separation phenomena in binary mixtures of Bose-Einstein condensates. The second one is to systems involving the fractional Laplacian.

MSC:

35J50 Variational methods for elliptic systems
35R11 Fractional partial differential equations
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