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
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.