Few results are available in the mathematical literature for studying the structure of the singular set of a weak solution u of F (x, u, Du) = 0. This paper provides new techniques to analyse such a set when u is semiconcave and F is a nonlinear convex function with respect to p. The main objective achieved here is a classification of the singularities of u that propagate along Lipschitz arcs. Such a propagation phenomenon is also described by means of a generalized characteristics inclusion.
Albano P., Cannarsa P. (2002). Propagation of singularities for solutions of nonlinear first order partial differential equations. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 162(1), 1-23 [10.1007/s002050100176].
Propagation of singularities for solutions of nonlinear first order partial differential equations
Albano P.;
2002
Abstract
Few results are available in the mathematical literature for studying the structure of the singular set of a weak solution u of F (x, u, Du) = 0. This paper provides new techniques to analyse such a set when u is semiconcave and F is a nonlinear convex function with respect to p. The main objective achieved here is a classification of the singularities of u that propagate along Lipschitz arcs. Such a propagation phenomenon is also described by means of a generalized characteristics inclusion.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
