Variational Techniques for Elliptic Partial Differential Equations: Theoretical Tools and Advanced Applications
About this ebook
Features
- A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields
- An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two
- Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc.
- A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics
About the author
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.
