Necessary p-th order optimality conditions for irregular Lagrange problem in calculus of variations

Abstract

The paper is devoted to singular calculus of variations problems with constraints which are not regular mappings at the solution point, e.i. its derivatives are not surjective. We pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we present necessary conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.