Volume: 31; 2019; 264 pp; Hardcover
MSC: Primary 35;
Print ISBN: 978-3-03719-191-0
Product Code: EMSTM/31
List Price: $58.00
AMS Member Price: $46.40
Estimates for Differential Operators in Half-space
Share this pageIgor W. Gel’man; Vladimir G. Maz’ya
Translated from the German by Darya Apushkinskaya.
Originally published in 1981 by Akademie-Verlag as Abschätzungen für Differentialoperatoren im Halbraum.
A publication of the European Mathematical Society
Inequalities for differential operators play a fundamental
role in the modern theory of partial differential equations. Among the
numerous applications of such inequalities are existence and
uniqueness theorems, error estimates for numerical approximations of
solutions and for residual terms in asymptotic formulas, as well as
results on the structure of the spectrum. The inequalities cover a
wide range of differential operators, boundary conditions and norms of
the corresponding function spaces.
The book focuses on estimates up to the boundary of a domain. It
contains a great variety of inequalities for differential and
pseudodifferential operators with constant coefficients. Results of
final character are obtained, without any restrictions on the type of
differential operators. Algebraic necessary and sufficient conditions
for the validity of the corresponding a priori estimates are
presented.
General criteria are systematically applied to particular types of
operators found in classical equations and systems of mathematical
physics (such as Lamé's system of static elasticity theory or
the the linearized Navier–Stokes system), Cauchy–Riemann's
operators, Schrödinger operators, among others. The well-known
results of Aronszajn, Agmon–Douglis–Nirenberg and
Schechter fall into the general scheme and sometimes are
strengthened.
The book will be interesting and useful to a wide audience,
including graduate students and specialists interested in the theory of
differential equations.
A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Readership
Graduate students and specialists interested in the theory of differential equations.