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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.

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
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