## On boundary value problems for first-order elliptic pseudosymmetric systems in $$\mathbb R^4$$.(English. Russian original)Zbl 1070.35010

Differ. Equ. 39, No. 3, 444-446 (2003); translation from Differ. Uravn. 39, No. 3, 410-412 (2003).
From the introduction: In a bounded domain $$\Omega\subset\mathbb{R}^4$$ whose boundary is a sufficiently smooth three-dimensional manifold $$\partial\Omega$$, we consider the boundary value problem of finding a solution $$U=U(x)$$ of the elliptic system of differential equations $\sum^4_{j=1}A_j\frac{\partial U} {\partial x_j}=f(x),\quad x\in\Omega,\tag{1}$ satisfying the boundary conditions ${\mathcal B}(y, \partial/\partial x)|_{x\to y}U=g(y),\quad y\in\partial\Omega. \tag{2}$ Here the $$A_j$$ $$(j=1,2,3,4)$$ are constant real matrices of the fourth order; moreover, $$A_1$$ is the identity matrix, and the remaining matrices are skew-symmetric, and $${\mathcal B}$$ is a $$2\times 4$$ matrix boundary operator consisting of scalar linear sufficiently smooth pseudodifferential operators “polynomial” in the normal to $$\partial\Omega$$. Theorem. For an arbitrary boundary operator $${\mathcal B}$$, the boundary value problem (1), (2) is not regularizable.

### MSC:

 35F15 Boundary value problems for linear first-order PDEs

### Keywords:

pseudodifferential boundary operator
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