Borsuk, Mikhail Transmission problems for elliptic second-order equations in non-smooth domains. (English) Zbl 1202.35001 Frontiers in Mathematics. Basel: Birkhäuser (ISBN 978-3-0346-0476-5/pbk; 978-3-0346-0477-2/ebook). xi, 218 p. (2010). The author investigates the behaviour of weak solutions to elliptic transmission problems in a neighborhood of boundary singularities: angular and conic points or edges.These problems are studied both for linear and quasi-linear equations.Let us point out that all the results are given in the book with complete proofs and are based on the author’s research he had made over the past years. Reviewer: Maria Alessandra Ragusa (Catania) Cited in 33 Documents MSC: 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35J40 Boundary value problems for higher-order elliptic equations 35J62 Quasilinear elliptic equations 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35R09 Integro-partial differential equations 35D30 Weak solutions to PDEs Keywords:elliptic equations; non-smooth domains; transmissions problems; weak solutions PDFBibTeX XMLCite \textit{M. Borsuk}, Transmission problems for elliptic second-order equations in non-smooth domains. Basel: Birkhäuser (2010; Zbl 1202.35001) Full Text: DOI