Abstract
Earlier, when considering reports on extremals with angular points, we assumed that the functions in them are continuous, and their derivatives are also continuous. But in most cases this condition is not met, and the decision is made in the form of extremals with corner points. Such reports include, for example5, a report on the reflection and refraction of extremes caused by the reflection and refraction of light. Similarly, discontinuous reports are divided into two types. In problems with a gap of the first kind, the fracture looks for extremes. In problems of the second kind, the state of the functional is investigated in the presence of a discontinuity of the function under the integral
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