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Elliptic equations in a two- or three-dimensional
bounded domain
may have singular solutions from the non-smoothness
of the
domain, changes of boundary conditions, and
discontinuities,
singularities of the coefficients. These
singularities give rise to
various difficulties in the theoretical analysis and
in the
development of numerical algorithms for these
equations. On the
other hand, most of the problems arising from physics,
engineering, and other applications have
singularities of this form.
In addition, the study on these elliptic equations
leads to good
understandings of other types of PDEs and systems of
PDEs. This
research, therefore, is not only of theoretical
interest, but also of
practical importance.
This book includes a-priori estimates
(well-posedness, regularity,
and Fredholm property) for these singular solutions
of general
elliptic equations in weighted Sobolev spaces, as
well as effective
finite element schemes and corresponding multigrid
estimates.
Graduate students and researchers will find it a very
useful
introductory reference.
bounded domain
may have singular solutions from the non-smoothness
of the
domain, changes of boundary conditions, and
discontinuities,
singularities of the coefficients. These
singularities give rise to
various difficulties in the theoretical analysis and
in the
development of numerical algorithms for these
equations. On the
other hand, most of the problems arising from physics,
engineering, and other applications have
singularities of this form.
In addition, the study on these elliptic equations
leads to good
understandings of other types of PDEs and systems of
PDEs. This
research, therefore, is not only of theoretical
interest, but also of
practical importance.
This book includes a-priori estimates
(well-posedness, regularity,
and Fredholm property) for these singular solutions
of general
elliptic equations in weighted Sobolev spaces, as
well as effective
finite element schemes and corresponding multigrid
estimates.
Graduate students and researchers will find it a very
useful
introductory reference.