On Properties of Minimizers to Some Variational Integrals
| Type of publication: | Misc |
| Citation: | |
| Publication status: | Submitted |
| 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 |
| Keywords: | fully stationary point., Noether equation, Nonlinear elliptic systems, variational integral |
| Authors | |
| Added by: | [JP] |
| Total mark: | 0 |
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