@article{oai:muroran-it.repo.nii.ac.jp:00009971,
 author = {TAKAHASHI,  Masatomo and 高橋, 雅朋},
 issue = {1},
 journal = {Journal of Mathematical Analysis and Applications},
 month = {May},
 note = {application/pdf, For families of hypersurfaces with singular points, a classical definition of an envelope is vague. In order to define an envelope for a family of hypersurfaces with singular points, we consider r-parameter families of frontals and of Legendre mappings in the unit tangent bundle over the Euclidean space. We define an envelope for the r-parameter family of Legendre mappings. Then the envelope is also a frontal. We investigate properties of the envelopes. As an application, we give a condition that the projection of a singular solution of a first order partial differential equation is an envelope.},
 pages = {408--420},
 title = {Envelopes of families of Legendre mappings in the unit tangent bundle over the Euclidean space},
 volume = {473},
 year = {2019},
 yomi = {タカハシ, マサトモ}
}