Semiregular corner singularities of smooth functions

The author considers $m$-corner singular points (boundary points for $m=1$) of smooth functions with nondegenerate second differentials, and studies bifurcation diagrams of functions (of corner singularities) and asymptotic representations of bifurcation conditional extremals (in the corner). For $m=2$, three soft bifurcations of conditional minima are described. Examples are given to illustrate potential applications of corner singularities of nonlinear variational equations of mathematical physics.
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