This article is cited in 3 papers

On boundary values of solutions of elliptic equations degenerating on the boundary

I. M. Petrushko


Abstract: Necessary and sufficient conditions are established for the existence, on the domain's boundary, of a limit in $\mathscr L_p$, $p>1$, of solutions of second order elliptic equations having Tricomi type degeneracy on the boundary.
Solvability of the Dirichlet problem for such an equation in spaces of type $W^1_{p,\mathrm{loc}}$ is proved.
Bibliography: 9 titles.

UDC: 517.956

MSC: 35J70

Received: 30.06.1987

 English version: Mathematics of the USSR-Sbornik, 1989, 64:1, 243–262

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