Singular Surfaces of Nonsmooth Solutions to Multiple Integral Variational Problems

Arik Melikyan
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Arik Melikyan: Institute for Problems in Mechanics, Russian Academy of Science

Chapter 8 in Generalized Characteristics of First Order PDEs, 1998, pp 263-289 from Springer

Abstract: 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.

Keywords: Shock Wave; Euler Equation; Integral Surface; Singular Surface; Singular Characteristic (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1758-9_9

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DOI: 10.1007/978-1-4612-1758-9_9

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