$A$-Solutions with singularities as almost solutions

V. M. Miklyukov

Sbornik. Mathematics, Tome 197 (2006) no. 11, pp. 1587-1605

Résumé

Almost solutions of quasilinear partial differential equations of the elliptic type are introduced. The class of equations under consideration contains, in particular, the equations of $p$-harmonic functions, the gas dynamic equation, and some other equations. Conditions ensuring that singular solutions to equations are almost solutions are indicated. Applications to the problem of removable singularities of solutions of elliptic equations and quasiregular maps are presented. The proofs are based on connections with differential forms. Bibliography: 32 titles.

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