Geodesic
The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 282-293

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of singularities appearing in generalized solutions of the boundary value Dirichlet problem for eikonal-type first-order partial differential equations is considered. The object of study is the pseudovertices of the boundary set. Finding the pseudovertices is an element of the procedure for constructing branches of the singular set. Necessary conditions of pseudovertex existence are obtained under weakened assumptions on the smoothness of the boundary of a nonconvex boundary set. The situation of the first-order smoothness of the boundary and breaks of the second-order derivatives is studied. The necessary conditions are written in terms of the stationarity of coordinate functions and with the use of one-sided curvatures.
Keywords: first-order PDE, minimax solution, diffeomorphism, curvature, optimal result function, singular set, symmetry.
Mots-clés : wavefront, eikonal 
@article{TIMM_2016_22_1_a27,
     author = {A. A. Uspenskii and P. D. Lebedev},
     title = {The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {282--293},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a27/}
}
TY  - JOUR
AU  - A. A. Uspenskii
AU  - P. D. Lebedev
TI  - The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2016
SP  - 282
EP  - 293
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a27/
LA  - ru
ID  - TIMM_2016_22_1_a27
ER  - 
%0 Journal Article
%A A. A. Uspenskii
%A P. D. Lebedev
%T The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set
%J Trudy Instituta matematiki i mehaniki
%D 2016
%P 282-293
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a27/
%G ru
%F TIMM_2016_22_1_a27
A. A. Uspenskii; P. D. Lebedev. The construction of singular curves for generalized solutions of eikonal-type equations with a curvature break in the boundary of the boundary set. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 282-293. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a27/