Hilbert's Nineteenth Problem - Nash's Theorem

Nash's Theorem

Nash gave a continuity estimate for solutions of the parabolic equation

where u is a bounded function of x1,...,xn, t defined for t ≥ 0. From his estimate Nash was able to deduce a continuity estimate for solutions of the elliptic equation

by considering the special case when u does not depend on t.

Read more about this topic:  Hilbert's Nineteenth Problem

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