Abstract:
The objective of this thesis is a proof of existence and uniqueness
of some partial differential equations. This is achieved via the energy
inequality, the method of functional analysis or the method of a prior
estimate depending on the density of the range. The proof is
accomplished after writing the partial differential equation in an
operator form and multiplying by an appropriate operator, so that the
resulting form leads to an energy inequality.
This energy inequality technique is very efficient, utilizing Sobolev
spaces. Several theories and inequalities from both functional analysis
and topology, have been used.
