Transmission Problems For Elliptic Second-order Equations In Non-smooth Domains (frontiers In Mathematics)
by Mikhail Borsuk /
2010 / English / PDF
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The goal of this book is to investigate the behavior 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 quasilinear (till now very little studied) equations. All results are given with complete proofs. A principal new feature of our work is the consideration of our estimates of weak solutions to the transmission problem for linear elliptic equations with minimal smooth coecients in ndimensional conic domains. Only few works are devoted to the transmission problem for quasilinear elliptic equations. Therefore, we investigate the weak solutions for general divergence quasilinear elliptic second-order equations in n-dimensional conic domains or in domains with edges. The basis of our research is the metod of integrodifferential inequalities. Such inequalities with exact estimating constants allow to establish possible or best possible estimates of solutions to boundary value problems for elliptic equations near singularities on the boundary. We prove new Friedrichs - Wirtinger type inequality and apply it to the investigation of the behavior of weak solutions to the transmission problem. The book will be of interest to specialists in elliptic boundary value problems and applications as well as to graduate students.
