BOUNDARY VALUE PROBLEMS FOR COMPOSITE TYPE EQUATIONS

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.