A regularity condition for generalized solutions of higher-order quasilinear elliptic equations

I. V. Skrypnik

Izvestiya. Mathematics, Tome 7 (1973) no. 6, pp. 1371-1421

Résumé

Regularity is proved for an arbitrary generalized solution of a quasilinear elliptic equation of divergent type which belongs to $W_2^{m+n/2}(\Omega')$, for an arbitrary strictly interior subregion $\Omega'$ of a region $\Omega$ ($2m$ is the order of the equation, and $n$ is the number of arguments). It follows from this, in particular, that the regularity problem has an affirmative solution in the two-dimensional case.

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