Difference Operators in Sobolev Spaces and Applications Prof. Alexander L. Skubachevskii, RUDN University, Russia
The theory of elliptic differential-difference equations has many interest-ing applications e.g. to
- the theory of sandwich shells and plates,
- the Kato problem concerning the analyticity of the square root of an analytic function of dissipative operators,
- nonlocal boundary value problems arising in plasma theory,
- the theory of multidimensional diffusion processes,
- nonlinear optics, …
This theory is based on the properties of difference operators acting in Sobolev spaces. Most important property of a regular difference operator:
It maps the Sobolev space of the first order with the homogeneous Dirichlet boundary condition onto the subspace of the Sobolev space of the first order with nonlocal boundary conditions continuously and bijectively. This result allows to reduce boundary value problems for strongly elliptic differential-difference equations to elliptic equations with nonlocal boundary conditions. Conversely, in some cases nonlocal elliptic boundary value problems can be reduced to elliptic differential-difference equations. Address Mathematikon Seminar Room 12 / 5th Floor Im Neuenheimer Feld 205 69120 Heidelberg Homepage Event www.iwr.uni-heidelberg.de/events Organizer Interdisciplinary Center for Scientific Computing (IWR) Homepage Organizer www.iwr.uni-heidelberg.de Contact Prof. Willi Jäger |