Partial Differential Equations

Introduction

1.Transmission Problems for Elliptic Second-Order Equations,by Mikhail Borsuk. [done]

2.Boundary Value Problem, by David L. Powers. [done]

3.The Mathematical Theory of Finite Element Methods, by Susanne C. Brenner & L.Ridgway Scott. [done]

4.First Course in PDE With Complex Variables and Transform Methods, by H.F.Weinberger.[done]

5.Partial differential equations I, by Taylor M.E. [done]

6.Elliptic Partial Differential Equations of Second Order, by D.Gilbarg & N.Trudinger [processing]

7.Potential Theory, by Lester Helms. [processing]

Step in Depth

1. Eigenvalue Problems of Laplace Equation, which is obvious an elliptic equation of second order.

For more detailed info, one can refer to the handouts on PDE Seminar:

Handout I

Handout II

2. Maximum Principle, which is always operational in complicated problems.

For more detailed info, one can refer to the handouts here.

Sophex: Cheng-Yau Gradient Estimate

3. Inverse Problem, which will be talked about in another page.