[en] Functional analysis and partial differential equations are two areas of mathematics that have a very strong connection but they are studied separately in the grade. In this work, we will study some great results of functional analysis, such as the open mapping theorem or the Hahn-Banach theorems, and we will also study the spaces where the solutions of partial differential equations live, the Sobolev spaces. We will see the inclusions that exists between them and under which conditions these solutions are regular or not. To do this, we will use functional analysis techniques and results, seeing this strong connection that exists between these two areas.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: María Jesús Carro Rossell