On solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space W_2^1 - Bozhonok, E. V. (Methods of Functional Analysis and Topology, 2007)
It is known, that if the Euler–Lagrange variational equation is fulfilled everywhere in classical case C^1 then it’s solution is twice continuously differentiable. The present note is devoted to the study of a similar problem for the Euler–Lagrange equation in the Sobolev space W_2^1.