Summary:
In this work, we present basic methods for the construction of energy-momentum
tensors. We investigate their geometric and physical significance and show that
using these tensors we can develop Derrick-Pohozaev identities and monotonicity
formulas. Also it is shown, how these results can be combined to
yield non-existence theorems for solutions of PDEs. A contribution of this work
is the remark that the so obtained Derrick-Pohozaev identity is possibly more
general, an issue requiring further investigation. By the investigation of the
subjects of this work, several issues evolved, requiring further investigation,
some of which are: energy-momentum tensors for problems with subsidiary
conditions, null Lagrangians, which may give a non-zero tensor, equivalence of
Euler-Lagrange and Noether equations, non-existence of stable solutions by
means of modification of Derrick’s method, energy-momentum tensors and
Derrick-Pohozaev identities for non-variational problems.
Keywords:
Calculus of variations, Energy-momentum tensor, Partial differential equations, Non-existence theory, Derrick-Pohozaev identity
