FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 937-941

**About correctness of the Dirichlet problem for
a multivariate elliptic system with varying coefficients**

G. A. Isaeva

Abstract

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```
The property of a system of partial differential equations with
variable coefficients to belong to one or another homotopic type
depends on
the domain point at which this system is considered. The degeneration
manifolds split the original region into parts. The study
of the influence of such degeneration on the solvability
character of the boundary value problems is important.
```

We consider the system of $n$ partial second order differential
equations

$$

- \Lambda(x) \Delta u_j + \mu \frac{\partial}{\partial x_j}

\sum_{i=1}^{n}\frac{\partial u_i}{\partial x_i} = 0,\quad
j = 1,\ldots,n,

$$

with a real function $\Lambda(x)$, $x = (x_1,\ldots,x_n)$.

We obtain the conditions, under which the modified Dirichlet problem for
this system is solvable up to an arbitrary harmonic function of $n - 1$
variables.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/993/99322t.htm

Last modified: November 11, 1999