Vladimir Kozlov

Izdannyj po blagosloveniju mitropolita Moskovskogo i vseja Rusi Kornilija albom vkljuchaet v sebja rasskaz ob istorii i vozrozhdenii Rogozhskoj Slobody-drevnego Dukhovnogo i istoricheskogo tsentra pravoslavnogo staroobrjadchestva v Moskve, nyneshnego vsemirnogo khranilischa dukhovnykh i materialnykh bogatstv staroobrjadtsev.

Dokumentalnoe issledovanie Vladimira Kozlova rasskazyvaet o pervoj v SSSR subkulture, volno ili nevolno vystupivshej protiv gospodstva kommunisticheskoj ideologii.

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.

This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: the first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented.Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems.Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order $2m$ in an angle.In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order $2$ in an $n$-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.

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.

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.

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.