discipline 
Pure Math

subject 
Linear partial
differential equations

lecturers 
László Simon 
credits 
2 
period 
1.and 2. Semester, 2 hours/week 
curriculum 
1. semester: Fourier transform of
tempered distributions. Fundamental solutions of linear partial differential
equations with constant coefficients. Sobolev
spaces: extension operators, trace operator. Characterization of Sobolev spaces by Fourier transform. Smoothness of
functions in Sobolev spaces. Existence and uniqueness of
weak solutions to boundary value problems for linear elliptic equations. Variational approach of boundary value problems and eigenvalue problems. 2. semester: Elliptic boundary value
problems with a parameter. Smoothness of the weak (variational)
solutions of elliptic problems. Initialboundary value problems for
hyperbolic and parabolic equations: Fourier method, Galerkin
method. Smoothness of solutions. 
literature 
R.E.
Showalter: Hilbert space method for partial differential equations. 
form of tuition 
lectures 
mode of assessment 
oral exam 