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@MISC{,
            author = {Bul{\'{\i}}{\v c}ek, Miroslav},
          keywords = {fully stationary point., Noether equation, Nonlinear elliptic systems, variational integral},
             title = {On Properties of Minimizers to Some Variational Integrals},
              year = {2013},
          abstract = {In the calculus of variations, the first usual discussed property of
a minimizer is the validity of the Euler-Lagrange equations which follows by
using the variations with respect to the variable - unknown. On the other
hand, doing the variations with respect to the independent variable - x one
can deduce the so-called Noether equations. Such a property is usually derived
under the additional hypothesis the the minimizer is a C1 function. Such a
minimizer is then also called the fully stationary point and the importance
of its existence naturally arises in many fields, in particular in the regularity
theory. In this short note we show that the restriction on the smoothness of
a minimizer is in fact not needed for the validity of the Noether equation and
we prove its validity for all minimizers for general class of variational problems
where only natural growth assumptions are required and/or for sufficiently
smooth (but not C1) solutions to the Euler-Lagrange equations.},
  Preprint project = {NCMM},
     Preprint year = {2013},
   Preprint number = {12},
       Preprint ID = {NCMM/2013/12}
}