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Elliptic Regularity Theory by Approximation Methods (Paperback)
Loot Price: R1,734
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Elliptic Regularity Theory by Approximation Methods (Paperback)
Series: London Mathematical Society Lecture Note Series
Expected to ship within 12 - 17 working days
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Presenting the basics of elliptic PDEs in connection with
regularity theory, the book bridges fundamental breakthroughs -
such as the Krylov-Safonov and Evans-Krylov results, Caffarelli's
regularity theory, and the counterexamples due to Nadirashvili and
Vladut - and modern developments, including improved regularity for
flat solutions and the partial regularity result. After presenting
this general panorama, accounting for the subtleties surrounding
C-viscosity and Lp-viscosity solutions, the book examines important
models through approximation methods. The analysis continues with
the asymptotic approach, based on the recession operator. After
that, approximation techniques produce a regularity theory for the
Isaacs equation, in Sobolev and Hoelder spaces. Although the Isaacs
operator lacks convexity, approximation methods are capable of
producing Hoelder continuity for the Hessian of the solutions by
connecting the problem with a Bellman equation. To complete the
book, degenerate models are studied and their optimal regularity is
described.
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