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.
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.File in questo prodotto:
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