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1. On solution uniqueness of the Dirichlet problem for a system of partial differential equations on one function in the unit ball

Author

Michail V. Beloglyadov and Vladimir P. Burskii

Subjects
Stochastic partial differential equation, Semi-elliptic operator, Dirichlet problem, symbols.namesake, Applied Mathematics, Dirichlet boundary condition, Mathematical analysis, First-order partial differential equation, symbols, Dirichlet's energy, Dirichlet series, Mathematics, Numerical partial differential equations
Abstract

In the present paper we consider a system of equations given for one unknown function that have generalized D'Alambert representation of solutions. We establish necessary and sufficient conditions for nontrivial solvability of the Dirichlet problem for such system in the unit ball. A simple necessary condition is obtained which says: for any i and j the angle between the vectors ai and aj must be a π-rational number.

Published
2011
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