Variational Techniques for Elliptic Partial Differential Equations: Theoretical Tools and Advanced Applications

ISBN-13: 9780367656645 / Angielski / Miękka / 2020 / 492 str.

Francisco J. Sayas; Thomas S. Brown; Matthew E. Hassell

Opis

This book, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations.

Spis treści

I Fundamentals

1 Distributions

2 The homogeneous Dirichlet problem

3 Lipschitz transformations and Lipschitz domains

4 The nonhomogeneous Dirichlet problem

5 Nonsymmetric and complex problems

6 Neumann boundary conditions

7 Poincare inequalities and Neumann problems

8 Compact perturbations of coercive problems

9 Eigenvalues of elliptic operators

II Extensions and Applications

10 Mixed problems

11 Advanced mixed problems

12 Nonlinear problems

13 Fourier representation of Sobolev spaces

14 Layer potentials

15 A collection of elliptic problems

16 Curl spaces and Maxwell's equations

17 Elliptic equations on boundaries

A Review material

B Glossary

O autorze

Francisco-Javier Sayas is a Professor of Mathematical Sciences at the University of Delaware. He has published over one hundred research articles in refereed journals, and is the author of Retarded Potentials and Time Domain Boundary Integral Equations.

Thomas S. Brown is a lecturer in Computational and Applied Mathematics at Rice University. He received his PhD in Mathematics from the University of Delaware in 2018, under the supervision of Francisco-Javier Sayas. His expertise lies in the theoretical and numerical study of elastic wave propagation in piezoelectric media with applications to control problems.

Matthew E. Hassell is a Systems Engineer at Lockheed Martin. He received his PhD in Applied Mathematics from the University of Delaware in 2016, under the supervision of Francisco-Javier Sayas, working on convolution quadrature techniques for problems in wave propagation and scattering by non-homogeneous media as well as viscous flow around obstacles.