ABSTRACT
In this section we will deal with boundary value problems associated to nonsymmetric bilinear forms, like the convection-diffusion equation − Δ u + b ⋅ ∇ u = f . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429507069/af768ad5-21aa-4c7b-88c6-5318b65e2dde/content/umath5_1.jpg"/> This will require proving a simple generalization of the Riesz-Fréchet representation theorem, dealing with nonsymmetric bounded and coercive bilinear forms. We will next extend our toolbox to complex vector spaces, working on the complexification of the Sobolev spaces we have defined in previous chapters.
