&bullet; <A HREF="http://www.worldscientific.com/worldscibooks/10.1142/2034">Geometry in Partial Differential Equations</A> (A. Pràstaro, Th.M. Rassias)

> This book emphasizes the interdisciplinary interaction in problems
> involving geometry and partial differential equations. It provides an
> attempt to follow certain threads that interconnect various approaches
> in the geometric applications and influence of partial differential
> equations. A few such approaches include: Morse-Palais-Smale theory in
> global variational calculus, general methods to obtain conservation
> laws for PDEs, structural investigation for the understanding of the
> meaning of quantum geometry in PDEs, extensions to super PDEs
> (formulated in the category of supermanifolds) of the geometrical
> methods just introduced for PDEs and the harmonic theory which proved
> to be very important especially after the appearance of the
> Atiyah-Singer index theorem, which provides a link between geometry
> and topology.

&bullet; <A HREF="http://math.stackexchange.com/questions/29942/what-connections-are-there-between-number-theory-and-partial-differential-equati">Number theory and partial differential equations</A> <I>(the answer given as a comment is noteworthy)</I>