Geodesic
Semiregular corner singularities of smooth functions
Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 151-163

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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. Figures 4. Bibliography: 29 titles. 
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Yu. I. Sapronov. Semiregular corner singularities of smooth functions. Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 151-163. http://geodesic.mathdoc.fr/item/SM_1991_68_1_a7/