Get BookSpectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations (Mathematical Surveys and Monographs)

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Book Details :
Published on: 2000-10-31
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Original language: English

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. [ihtik.lib.ru] _ [ihtik.lib.ru] _. : 14292 : 573 GB; ; d:\_ihtik.lib.ru\2012.03 ... web.mit.edu / jik/src/Attic/kerberos_ password - . .mn 0 01 05_1 1 10 100 10th 11 11_d0003 12 13 14 141a 143b 15 16 17 17igp 18 19 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 ... Le Live Marseille : aller dans les plus grandes soires ... Retrouvez toutes les discothque Marseille et se retrouver dans les plus grandes soires en discothque Marseille. Oxbridge essays scampi shrimp recipe nobu-zzvc Oxbridge essays scampi shrimp recipe nobu-zzvc Samedi 14 mar 2015
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