On a generalization of the Darboux theorem to the multidimensional case
M. V. Korobkov

This publication is cited in the following articles:

1. M. V. Korobkov, “Properties of $C^1$-smooth mappings with one-dimensional gradient range”, Siberian Math. J., 50:5 (2009), 874–886            
2. M. V. Korobkov, E. Yu. Panov, “Necessary and sufficient conditions for a curve to be the gradient range of a $C^1$-smooth function”, Siberian Math. J., 48:4 (2007), 629–647              
3. M. V. Korobkov, E. Yu. Panov, “Isentropic solutions of quasilinear equations of the first order”, Sb. Math., 197:5 (2006), 727–752              
4. Korobkov M.V., Panov E.Yu., “Necessary and sufficient conditions for a curve to be an image of the gradient of a C–1 function”, Doklady Mathematics, 74:2 (2006), 696–699            
5. Korobkov M., “On stability of a class of convex functions”, Progress in Analysis, 2003, 207–213      
6. Korobkov M.V., “To extension of the Lagrange and Darboux theorems over vector-valued functions”, Doklady Mathematics, 63:2 (2001), 227–229    
7. Korobkov M.V., Egorov A.A., “Stability of classes of Lipschitzian mappings, the Darboux theorem, and quasiconvex sets”, Doklady Mathematics, 62:1 (2000), 84–88