For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, this second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this book are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the...
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elli...
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain....
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of ellipti...
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...
This volume is dedicated to the centenary of the outstanding mathematician of the 20th century, Sergey Sobolev, and, in a sense, to his celebrated ...
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...
There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples inc...
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
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...
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.
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...
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...
Vladimir Maz'ya (born 1937) is an outstanding mathematician who systematically made fundamental contributions to a wide array of areas in mathematical...
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...
In the present book the conditions are studied for the semi-boundedness of partial differential operators which is interpreted in different way...
This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory, approximation theory, and reflects the broad spectrum of Roland Duduchava's research. The book is addressed to a wide audience of pure and applied mathematicians.
This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on...
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.
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...
