Around the Research of Vladimir Maz'ya II
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.
Professor Maz'ya has received numerous awards for his outstanding contributions, in particular, the Humboldt Research Prize (1999), the Verdaguer Prize of the French Academy of Sciences (2003)He was elected to the Royal Society of Edinburgh (2001) and the Royal Swedish Academy of Sciences (2002)Several international conferences were organised for the occasion of his 60th birthdayThere are several collections of papers honored Prof. Maz'ya. Prof. Maz'ya published more than 20 monographs and more than 450 articles. The range of his interests is very wide and many of his results play a key role in many areas of analysis and PDEs.Nevertheless, the presented volume is absolutely different from all published books honored V. Maz'ya:It focuses on the current state of research in analysis, PDEs and function theory, detailing recent advances, selected in relation to Mazy’as results.All the results are new and never published earlierThe mentioned collections present proceedings of conferences in honor of V. Maz'ya and contributors are participants of these conferences. In this volume contributors and contributions were selected in accordance with the main idea of the volume