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Advanced Course on Pseudodifferential Operators and

Their Applications 1

Date: 18-28 April, 1998

Location: TICMI (Tbilisi)

Roland Duduchava (Razmadze Mathematical Institute, Georgian Academy of Sciences)

PSEUDODIFFERENTIAL EQUATIONS ON MANIFOLDS WITH SMOOTH BOUNDARY: SOLVABILITY, ASYMPTOTICS OF SOLUTIONS, APPLICATIONS

Summary: Pseudodifferential operators (PsDOs) on manifolds (definition, properties). Boundedness of PsDOs in anisotropic Sobolev spaces with weight. Factorization of matrix elliptic symbols and Fredholm properties of PsDOs. Asymptotics of solutions to elliptic systems of pseudodifferential equations. Application to some problems in elasticity.

B.-Wolfgang Schulze (University of Potsdam, Germany)

THE PSEUDODIFFERENTIAL CALCULUS FOR SINGULAR AND DEGENERATE OPERATORS

Summary: The lectures present the basic methods of PsDOs for solving elliptic and parabolic problems on configurations with singularities (conical, edge, corners, cuspidal etc.). Essential tools are the Mellin transform, meromorphic operator-valued symbols and weighted wedge Sobolev spaces with asymptotics. The calculus is aimed at constructing parametrices or inverses with the calculus and to illustrate the connection to concrete models in applied sciences.

Coordinator: George Jaiani

This course is suitable for advanced graduate students or recent Ph.D.'s. The participants will also have an opportunity to give 20-minute talks on their own work at a mini-symposium which will take place during the Advanced Course. Lectures and abstracts of the talks will be published and distributed among the lecturers and participants after Advanced Course. The registration fee for participants is 400 USD which includes all local expenses during the Advanced Course. A restricted number of participants will be awarded grants.

Further information: TICMI, I.Vekua Institute of Applied Mathematics of Tbilisi State University, University Str. 2, Tbilisi 380043, Georgia

e.mail: jaiani@viam.sci.tsu.ge

Tel.:+995 32 305995