Solution of one boundary value problem for curl, +λ I operator in the ball

Abstract

The boundary value problem for the linear weakly elliptic system

in the ball G of

is studied and three methods for finding the solution of it in the space

are derived. In order to reach this goal, it is used with the theory of potentials, spectral theory and a complex form of this system is considered.

Keywords:

• Boundary value problems for partial differential equations
• First- and second-order elliptic partial differential equations
• Spectral theory of partial differential operators
• 2000 Mathematics Subject Classifications: 35J55
• 35J25
• 35P05

Acknowledgments

The main part of this article was written while the authors met at the Institute of Mathematics of the Freie Universität Berlin (during Prof. R. Saks' DAAD (Deutsche Akademische Austauschdienst) fellowship tenure and Prof. C.J. Vanegas' sabbatical year). The authors would like to thank Prof. Heinrich Begehr for his support and hospitality.

Notes

Dedicated to Professor Heinrich Begehr on his 65th birthday.

Additional information

Notes on contributors

C. J. Vanegas

Dedicated to Professor Heinrich Begehr on his 65th birthday.