# American Institute of Mathematical Sciences

November  2013, 33(11&12): 5457-5491. doi: 10.3934/dcds.2013.33.5457

## Hardy type inequalities and hidden energies

 1 Departamento de Matemáticas and ICMAT. Universidad Autónoma de Madrid, Cantoblanco. 28049 Madrid, Spain 2 Department of Mathematics & Engineering Sciences, Hellenic Army Academy, 16673, Athens, Greece

Received  January 2012 Published  May 2013

We obtain new insights into Hardy type Inequalities and the evolution problems associated to them. Surprisingly, the connection of the energy with the Hardy functionals is nontrivial, due to the presence of a Hardy singularity energy. This corresponds to a loss for the total energy. These problems are defined on bounded domains or the whole space.
We also consider equivalent problems with inverse square potential on exterior domains or the whole space. The extra energy term is then present as an effect that comes from infinity, a kind of hidden energy. In this case, in an unexpected way, this term is additive to the total energy, and it may even constitute the main part of it.
Citation: Juan Luis Vázquez, Nikolaos B. Zographopoulos. Hardy type inequalities and hidden energies. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5457-5491. doi: 10.3934/dcds.2013.33.5457
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