Phase Transition for Potentials of High-Dimensional Wells
نویسندگان
چکیده
For a potential function F W R ! RC that attains its global minimum value at two disjoint compact connected submanifolds N in R , we discuss the asymptotics, as ! 0, of minimizers u of the singular perturbed functional E .u/ D R .jruj 2 C 1 2 F.u//dx under suitable Dirichlet boundary data g W @ ! R . In the expansion of E .u / with respect to 1 , we identify the first-order term by the area of the sharp interface between the two phases, an area-minimizing hypersurface , and the energy c 0 of minimal connecting orbits between N and N , and the zerothorder term by the energy of minimizing harmonic maps into N both under the Dirichlet boundary condition on @ and a very interesting partially constrained boundary condition on the sharp interface . © 2011 Wiley Periodicals, Inc.
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