Necessary and sufficient conditions for a curve to be the gradient range of a C1-smooth function |
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| Authors: | M. V. Korobkov E. Yu. Panov |
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| Affiliation: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia;(2) Novgorod State University, Velikiĭ Novgorod, Russia |
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| Abstract: | We find some necessary and sufficient conditions for a plane curve to be the gradient range of a C 1-smooth function of two variables. As one of the consequences we give the necessary and sufficient conditions on a continuous function ? under which the differential equation (frac{{partial v}}{{partial t}} = varphi left( {frac{{partial v}}{{partial x}}} right)) has nontrivial C 1-smooth solutions. |
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| Keywords: | C 1-smooth function gradient range curve |
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