Transmission problems for elliptic second-order equations in non-smooth domains

The goal of this book is to investigate the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges. We consider this problem both for linear and quasi-linear (till now very little studied) equations. Chapter 1 is of auxiliary character. Chapter 2 deals with the eigenvalue problem for the m-Laplace-Beltrami operator. By the variational principle we prove a new integro-differential Friedrichs-Wirtinger type inequality. This inequality is a basis for theobtaining of precise exponents of the decreasing rate of the solution near boundary singularities. Chapter 3 deals with the investigation of the transmission problem for linear elliptic second order equations in the domains with boundary conic point. Chapter 4 is devoted to the transmission problem in conic domains with N different media for an equation with the Laplace operator in the principal part. Chapters 5, 6 and 7 deal with the investigation of the transmission problem for quasi-linear elliptic second order equations in the domains with boundary conic point or with an edge at the boundary of a domain. Estimates of weak solutions to the transmission problem for linear elliptic equationswith minimal smooth coefficients in n-dimensional conic domains Investigationof weak solutions for general divergence quasi-linear elliptic second-order equations in n-dimensional conic domains or in domains with edges INDICE: Preface.- Introduction.- 1 Preliminaries.- 2 Eigenvalue problem and integro-differential inequalities.- 3 Best possible estimates of solutions to the transmission problem for linear elliptic divergence second order equations in a conical domain.- 4 Transmission problem for the Laplace operator with N different media.- 5 Transmission problem for weak quasi-linear elliptic equations in a conical domain.- 6 Transmission problem for strong quasi-linear elliptic equations in a conical domain.- 7 Best possible estimates of solutions to the transmission problem for a quasi-linear elliptic divergence second orderequation in a domain with a boundary edge.- Bibliography.- Index.- Notation Index.

• ISBN: 978-3-0346-0476-5
• Editorial: Birkhaüser
• Encuadernacion: Rústica
• Páginas: 200
• Fecha Publicación: 01/04/2010
• Nº Volúmenes: 1
• Idioma: Inglés