The asymptotic analysis of boundary value problems in parameter-dependent domains is a rapidly developing field of research in the theory of partial differential equations, with important applications in electrostatics, elasticity, hydrodynamics and fracture mechanics. Building on the work of Ciarlet and Destuynder, this book provides a systematic coverage of these methods in multi-structures, i.e. domains which are dependent on a small parameter e in such a way that the limit region consists of subsets of different space dimensions. An undergraduate knowledge of partial differential equations and functional analysis is assumed.

Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs)

Science & Math

Movchan, Alexander

Maz'ya, Vladimir

Kozlov, Vladimir

Mathematics

Oxford University Press

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II: Volume II (Operator Theory: Advances and Applications)

Crafts, Hobbies & Home

Nazarov, Serguei

Plamenevskij, Boris

Gardening & Landscape Design

Birkhauser

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains: Volume I (Operator Theory: Advances and Applications)

There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green’s kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables. This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.

Green's Kernels and Meso-Scale Approximations in Perforated Domains (Lecture Notes in Mathematics, 2077)

Nieves, Michael

Springer

Vladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. In this fascinating book he describes the first thirty years of his life. He starts with the story of his family, speaks about his childhood, high school and university years, describe his formative years as a mathematician. Behind the author's personal recollections, with his own joys, sorrows and hopes, one sees a vivid picture of the time. He speaks warmly about his friends, both outside and inside mathematics. The author describes the awakening of his passion for mathematics and his early achievements. He mentions a number of mathematicians who influenced his professional life. The book is written in a readable and inviting way sometimes with a touch of humor. It can be of interest for a very broad readership.

Differential Equations of My Young Years

​In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different ways. Nowadays one knows rather much about L2-semibounded differential and pseudo-differential operators, although their complete characterization in analytic terms causes difficulties even for rather simple operators. Until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. The goal of the present book is to partially fill this gap. Various types of semi-boundedness are considered and some relevant conditions which are either necessary and sufficient or best possible in a certain sense are given. Most of the results reported in this book are due to the authors.

Semi-bounded Differential Operators, Contractive Semigroups and Beyond (Operator Theory: Advances and Applications, 243)

Cialdea, Alberto

In this book, Vladimir Maz'ya describes the first thirty years of his life. He describes his formative years in the Soviet Union, the awakening of his passion for mathematics and his early achievements, presenting, in the process, a vivid picture of the time.

This trail-blazing treatment of a new and emerging topic sets out the authors' own research into differing interpretations of the semi-boundedness of partial differential operators. It examines function spaces that include the Hilbert and Banach varieties.

The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.

Differential Equations with Operator Coefficients: with Applications to Boundary Value Problems for Partial Differential Equations (Springer Monographs in Mathematics)

The first part of this book offers a comprehensive overview of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The second part of the book explores several applications of this theory.

Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften, 337)

Shaposhnikova, Tatyana O.

See the best price to sell, buy, or rent books by Maz'ya, Vladimir. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Maz'ya, Vladimir

See the best price to sell, buy, or rent books by Maz'ya, Vladimir. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Asymptotic Analysis of Fields in Multi-Structures (Oxford Mathematical Monographs)

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II: Volume II (Operator Theory: Advances and Applications)

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains: Volume I (Operator Theory: Advances and Applications)

Green's Kernels and Meso-Scale Approximations in Perforated Domains (Lecture Notes in Mathematics, 2077)

Differential Equations of My Young Years

Semi-bounded Differential Operators, Contractive Semigroups and Beyond (Operator Theory: Advances and Applications, 243)

Differential Equations of My Young Years

Semi-bounded Differential Operators, Contractive Semigroups and Beyond (Operator Theory: Advances and Applications, 243)

Differential Equations with Operator Coefficients: with Applications to Boundary Value Problems for Partial Differential Equations (Springer Monographs in Mathematics)

Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften, 337)