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Singular Surfaces of Nonsmooth Solutions to Multiple Integral Variational Problems

In: Generalized Characteristics of First Order PDEs

Author

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  • Arik Melikyan

    (Institute for Problems in Mechanics, Russian Academy of Science)

Abstract

In this chapter we consider one more (the third) class of problems where singular characteristics describe the singular surfaces, this time for the solution to a second order PDE. These characteristics can be understood either as singular ones, related to some appropriate first order PDE, or as generalized characteristics introduced in Chapter 1 and related directly to the second order PDE, the Euler equation for a variational problem. In the latter case the manifold W and corresponding singular Hamiltonian are defined using generalized Weierstrass-Erdmann conditions and the solution continuity condition.

Suggested Citation

  • Arik Melikyan, 1998. "Singular Surfaces of Nonsmooth Solutions to Multiple Integral Variational Problems," Springer Books, in: Generalized Characteristics of First Order PDEs, chapter 8, pages 263-289, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1758-9_9
    DOI: 10.1007/978-1-4612-1758-9_9
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