Lectures on Partial Differential Equations
www.dam.brown.edu › people › menoncontexts. The main sources for this chapter are John [7, Ch. 6] and Gilbarg and Trudinger [5, Ch. 2]. 1.1.1 Minimal surfaces and Laplace’s equation First the geometric context. Take a closed wire frame, dip it in soap solution and pull it out. What is the shape of the soap film? One mathematical formulation of this problem is the following.
Elliptic Partial Differential Equations of Second Order
https://d-nb.info/960025553/04David Gilbarg • Neil S.Trudinger Elliptic Partial Differential Equations of Second Order Reprint of the 1998 Edition Springer. Table of Contents Chapter 1. Introduction 1 ... Generalized Solutions and Regularity 177 8.1. The Weak Maximum Principle 179 8.2. Solvability of the Dirichlet Problem 181 8.3. Differentiability of Weak Solutions 183