His first main works were devoted to the well-posedness of the Cauchy problem for weakly hyperbolic equations. In particular he discovered a necessary (later proven to be sufficient) condition for Cauchy problem to be well-posed no matter what the lower terms in the equation are.[5]
Propagation of singularities
In a series of papers he explored propagation of singularities of symmetric hyperbolic systems inside of the domain and near the boundary. He was invited to give a talk at ICM—1978, Helsinki but was not granted an exit visa by the Soviet authorities;[6] however his talk [7] was published in the Proceedings of the Congress.
Asymptotic distribution of eigenvalues
His work in propagation of singularities logically guided him to the theory of asymptotic distribution of eigenvalues (a subject he has been studying ever since). V. Ivrii's debut in this field was a proof of Weyl conjecture (1980). Then he developed a rescaling technique which allowed to consider domains and operators with singularities. He again was invited give a talk at ICM—1986, Berkeley but again was not granted an exit visa by the Soviet authorities. His talk [8] was read by Lars Hörmander and published in the Proceedings of the Congress.
V. Ivrii wrote three research monographs,[9][10] and,[11] all published by Springer-Verlag.
Multiparticle quantum theory
The methods developed by V. Ivrii were very useful for the rigorous justification of Thomas-Fermi theory. Together with Israel Michael Sigal he justified the Scott correction term for molecules.[12] Later V. Ivrii justified the Dirac and Schwinger correction terms.
