The first volume of the monograph series “Problems and methods: mathematics, mechanics, cybernetics” contains I.V.Skrypnik’s selected works in which the following questions are studied: A-harmonic forms on a Riemannian manifold, regularity of solutions of quasilinear elliptic high-order equations, topological methods of investigation of solvability of nonlinear equations, quasilinear high-order equations with strengthened ellipticity, regularity of a boundary point for quasilinear equations, point-wise estimates of solutions of model nonlinear problems and homogenization of nonlinear Dirichlet problems in domains with composite structure.
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