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Removable singularities of solutions of elliptic equations. (English. Russian original) Zbl 1183.35144

J. Math. Sci., New York 160, No. 1, 61-83 (2009); translation from Sovrem. Mat. Prilozh. 57 (2008).
The present paper is an overview of results devoted to metric conditions for removability of closed sets for solutions of homogeneous partial differential equations in various function classes. The author considers equations with a quasi-homogeneous semi-elliptic operator and with constant coefficients, linear second-order uniformly elliptic equations in the divergent form with real bounded measurable coefficients, quasilinear equations with the \(p\)-Laplacian, and the minimal surface equation.

MSC:

35J61 Semilinear elliptic equations
35J62 Quasilinear elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
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