Textbook for Partial Differential Equations with a viewpoint towards Geometry.

Though similar questions have been asked at Good 1st PDE book for self study and Good reference texts for introduction to partial differential equation? but none of them really answer my query, so I am bounded to ask this.

I am basically interested in Differential and Riemannian Geometry and one of my Professors told me that it will be a good idea if I acquire a sound knowledge of PDE. I know about the basics of PDE (i.e., methods of solving PDE ) but I don't have any firm knowledge of the analysis which goes on in there.

So, my question is that what will be a good textbook to start learning PDE that could help in undrstanding the $\it{analysis}$ portion as well as with applications of PDE in Differential/Riemannian Geometry.

Background : I have studied Measure Theory, Functional Analysis, Complex Analysis and some Fourier Analysis (from Stein & Shakarchi's book on Fourier Analysis). I am currently studying Algebraic Topology, Differential and Riemannian Geometry (from Do Carmo's book).

Thanks!!

• It doesn't quite fit the bill, but I really liked Arnold's book. – user137731 Sep 27 '14 at 19:31