On Dirichlet problem for a second order equation without type. (Russian. English summary) Zbl 1164.35451

Burskii, V. P.; Kirichenko, E. V.

Nonlinear Bound. Value Probl. 17, 20-30 (2007).

Summary: In present paper it is considered the first boundary value problem for a second order differential equation with constant coefficients and inhomogeneous symbol in a plane corner. It is obtained the necessary and sufficient condition of uniqueness of solution of this problem in the space \(C^2\) with polynomial growth at infinity.

MSC:

35M99	Partial differential equations of mixed type and mixed-type systems of partial differential equations
35E15	Initial value problems for PDEs and systems of PDEs with constant coefficients
35E20	General theory of PDEs and systems of PDEs with constant coefficients

Keywords:

equation without a type; corner point; uniqueness