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The paper studies solutions of ODEs killed on the domain boundary and theirfirst exit times from the domain. Some regularity is obtained in the form ofestimates of L_2-norm for functionals on solutions and the first exit times.Some regularity properties for the density of solutions killed on the boundaryis also studied for the case of random initial conditions.

Dokuchaev, N.G. The integral estimations for ordinary differential equations with a discontinuity on a domain boundary