1 Table of Contents: “... -- 17 More General Partial Differential Equations -- 18 Green's Functions and Dirichlet's Principle...”

2 Table of Contents: “... -- Appendices: A1. Dirichlet principle -- A2. Uniqueness theorem for contracting mapping -- A3. On separating...”

3 “...'s rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he...”

4 Table of Contents: “..., and Brownian Motion -- The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence...”

5 Table of Contents: “... Equations -- The Heat Equation, Semigroups, and Brownian Motion -- The Dirichlet Principle. Variational...”

6 Table of Contents: “... Differential Equations -- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence...”

7 Table of Contents: “... of Important Notions -- 2 Hilbert Spaces, Orthogonality, and the Dirichlet Principle -- 2.1 Hilbert Spaces...”

8 Table of Contents: “... -- Bernhard Riemann -- Riemann’s Doctoral Dissertation. The Dirichlet Principle -- Conformal Mappings -- Karl...”

9 Table of Contents: “... The Dirichlet Principle and Sobolev Spaces -- 20 Hardy Spaces on the Disk -- 1 Definitions and Elementary...”

10 Table of Contents: “... and Teichmüller Space -- 5 Teichmüller theory and Plateau—Douglas problem -- 6 Rescuing Riemann’s Dirichlet...”