New results, presented from world-recognized experts, are close to scientific interests of Professor Maz'ya and use, directly or indirectly, the fundamental influential Maz'ya's works penetrating, in a sense, the theory of PDEs. In particular, the following topics are covered: semilinear elliptic equations with exponential monlinearity, stationary Navier-Stokes equations on Lipschitz domains in Riemannian manifolds, Stokes equations in a thin cylindrical elastic tube the Neumann problem for 4th order linear partial differential operators the Stokes system in convex polyhedra, periodic scattering problems, integral equations for harmonic single layer potential on the boundary of a domain with cusp. Homogenization methods, methods of multiscale expansions, matched asymptotic expansions are applied for studying PDEs, problems with perturbed boundary at a conic point, etc. Singular perturbations arising in elliptic shells, positive solutions of semilinear elliptic inequalities on Riemannian manifolds, the regularity for nonlinear subelliptic equations, and the regularity of boundary points are discussed.
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