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...

Professor Maz'ya - one of the main developers of the modern theory of Sobolev spaces - contributed to the theory in many various directions. The strong influence of his fundamental works is traced in recent results presented in this volume from world-recognized specialists. The topics cover various aspects of the theory of function spaces, including Orlicz-Sobolev spaces, weighted Sobolev spaces, Dirichlet spaces, Besov Spaces with negative exponents, fractional Sobolev spaces on half-spaces and sharp constants in the Hardy inequality, Maz'ya's capacitary analogue of the co-area inequality...

Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of...

This volume is dedicated to the centenary of the outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated work On a theorem of functional analysis, published in 1938, exactly 70 years ago, was where the original Sobolev inequality was proved. This double event is a good occasion to gather experts for presenting the latest results on the study of Sobolev inequalities, which play a fundamental role in analysis, the theory of partial differential equations, mathematical physics, and differential geometry. In particular, the following topics are...

Mathematical Problems from Applied Logic I presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. An overview of the current state as well as open problems and perspectives are clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics, and computability theory. The book contains interesting contributions concerning the role...

"Mathematical Problems from Applied Logic II" presents chapters from selected, world renowned, logicians. Important topics of logic are discussed from the point of view of their further development in light of requirements arising from their successful application in areas such as Computer Science and AI language. Fields covered include: logic of provability, applications of computability theory to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based...

In this authoritative and comprehensive volume, Claude Bardos and Andrei Fursikov have drawn together an impressive array of international contributors to present important recent results and perspectives in this area. The main subjects that appear here relate largely to mathematical aspects of the theory but some novel schemes used in applied mathematics are also presented. Various topics from control theory, including Navier-Stokes equations, are covered.

Stability is a very important property of mathematical models simulating physical processes which provides an adequate description of the process. Starting from the classical notion of the well-posedness in the Hadamard sense, this notion was adapted to different areas of research and at present is understood, depending on the physical problem under consideration, as the Lyapunov stability of stationary solutions, stability of specified initial data, stability of averaged models, etc.

The stability property is of great interest for researchers in many fields such as mathematical...

The topics of this volume are diverse, but all of them are related to a huge area in analysis and applications where remarkably deep results and original approaches of Professor Maz'ya play a fundamental role. World-recognized experts present their new results covering, in particular, the following topics: Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-dissipativity connected with the Lp-contractivity of the generated semigroups, optimal control of a biharmonic obstacle problem sharp bilateral bounds of Green's function for the...