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For the first time in the mathematical literature this
two-volume work introduces a unified and general approach to the
asymptotic analysis of elliptic boundary value problems in
singularly perturbed domains. While the first volume is devoted to
perturbations of the boundary near isolated singular points, this
second volume treats singularities of the boundary in higher
dimensions as well as nonlocal perturbations.
At the core of this book are solutions of elliptic boundary value
problems by asymptotic expansion in powers of a small parameter
that characterizes the perturbation of the domain. In particular,
it treats the important special cases of thin domains, domains with
small cavities, inclusions or ligaments, rounded corners and edges,
and problems with rapid oscillations of the boundary or the
coefficients of the differential operator. The methods presented
here capitalize on the theory of elliptic boundary value problems
with nonsmooth boundary that has been developed in the past thirty
years.
Moreover, a study on the homogenization of differential and
difference equations on periodic grids and lattices is given. Much
attention is paid to concrete problems in mathematical physics,
particularly elasticity theory and electrostatics.
To a large extent the book is based on the authors work and has no
significant overlap with other books on the theory of elliptic
boundary value problems.
"
For the first time in the mathematical literature this
two-volume work introduces a unified and general approach to the
asymptotic analysis of elliptic boundary value problems in
singularly perturbed domains. While the first volume is devoted to
perturbations of the boundary near isolated singular points, this
second volume treats singularities of the boundary in higher
dimensions as well as nonlocal perturbations.
At the core of this book are solutions of elliptic boundary value
problems by asymptotic expansion in powers of a small parameter
that characterizes the perturbation of the domain. In particular,
it treats the important special cases of thin domains, domains with
small cavities, inclusions or ligaments, rounded corners and edges,
and problems with rapid oscillations of the boundary or the
coefficients of the differential operator. The methods presented
here capitalize on the theory of elliptic boundary value problems
with nonsmooth boundary that has been developed in the past thirty
years.
Moreover, a study on the homogenization of differential and
difference equations on periodic grids and lattices is given. Much
attention is paid to concrete problems in mathematical physics,
particularly elasticity theory and electrostatics.
To a large extent the book is based on the authors work and has no
significant overlap with other books on the theory of elliptic
boundary value problems.
"
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