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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Harnack's Inequality for Degenerate and Singular Parabolic Equations (Hardcover, 2012 Ed.)
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Harnack's Inequality for Degenerate and Singular Parabolic Equations (Hardcover, 2012 Ed.)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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Degenerate and singular parabolic equations have been the subject
of extensive research for the last 25 years. Despite important
achievements, the issue of the Harnack inequality for non-negative
solutions to these equations, both of p-Laplacian and porous medium
type, while raised by several authors, has remained basically open.
Recently considerable progress has been made on this issue, to the
point that, except for the singular sub-critical range, both for
the p-laplacian and the porous medium equations, the theory is
reasonably complete. It seemed therefore timely to trace a
comprehensive overview, that would highlight the main issues and
also the problems that still remain open. The authors give a
comprehensive treatment of the Harnack inequality for non-negative
solutions to p-laplace and porous medium type equations, both in
the degenerate (p2 or m1) and in the singular range (1p<2 or
0m<1), starting from the notion of solution and building all the
necessary technical tools. The book is self-contained. Building on
a similar monograph by the first author, the authors of the present
book focus entirely on the Harnack estimates and on their
applications: indeed a number of known regularity results are given
a new proof, based on the Harnack inequality. It is addressed to
all professionals active in the field, and also to advanced
graduate students, interested in understanding the main issues of
this fascinating research field.
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