David Edmunds is an analyst who has been at the University of Sussex since 1966 where he is currently Emeritus Professor. His interests include function spaces, interpolation theory, entropy and s-numbers, and elliptic partial differential equations.Desmond Evans is Emeritus Professor at the University of Cardiff, having been at Cardiff since 1964. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and mathematical physics. These related areas include the properties of function spaces and the mappings between them, growth and asymptotic estimates for eigenvalues and s-numbers, and inequalities.

• 1. Preliminaries.- 2. The Laplace Operator.- 3. Second-order elliptic equations.- 4. The classical Dirichlet problem for second-order elliptic operators.- 5. Elliptic operators of arbitrary order.- 6. Operators and quadratic forms in Hilbert space.- 7. Realisations of second-order linear elliptic operators.- 8. The Lp approach to the Laplace operator.- 9. The p-Laplacian.- 10. The Rellich inequality.- 11. More properties on Sobolev embeddings.- 12. The Dirac Operator.

“The book is well-written … . The presentation is self-contained and unified. … The book will be of interest to graduate students and to all researchers in PDEs.” (Petar Popivanov, zbMATH 1436.35003, 2020)

David Edmunds is an analyst who has been at the University of Sussex since 1966 where he is currently Emeritus Professor. His interests include function spaces, interpolation theory, entropy and s-numbers, and elliptic partial differential equations.Desmond Evans is Emeritus Professor at the University of Cardiff, having been at Cardiff since 1964. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and mathematical physics. These related areas include the properties of function spaces and the mappings between them, growth and asymptotic estimates for eigenvalues and s-numbers, and inequalities.

• 1. Preliminaries.- 2. The Laplace Operator.- 3. Second-order elliptic equations.- 4. The classical Dirichlet problem for second-order elliptic operators.- 5. Elliptic operators of arbitrary order.- 6. Operators and quadratic forms in Hilbert space.- 7. Realisations of second-order linear elliptic operators.- 8. The Lp approach to the Laplace operator.- 9. The p-Laplacian.- 10. The Rellich inequality.- 11. More properties on Sobolev embeddings.- 12. The Dirac Operator.

“The book is well-written … . The presentation is self-contained and unified. … The book will be of interest to graduate students and to all researchers in PDEs.” (Petar Popivanov, zbMATH 1436.35003, 2020)

David Edmunds is an analyst who has been at the University of Sussex since 1966 where he is currently Emeritus Professor. His interests include function spaces, interpolation theory, entropy and s-numbers, and elliptic partial differential equations.Desmond Evans is Emeritus Professor at the University of Cardiff, having been at Cardiff since 1964. His main research interests are in the spectral theory associated with differential equations and related areas of analysis and mathematical physics. These related areas include the properties of function spaces and the mappings between them, growth and asymptotic estimates for eigenvalues and s-numbers, and inequalities.

• 1. Preliminaries.- 2. The Laplace Operator.- 3. Second-order elliptic equations.- 4. The classical Dirichlet problem for second-order elliptic operators.- 5. Elliptic operators of arbitrary order.- 6. Operators and quadratic forms in Hilbert space.- 7. Realisations of second-order linear elliptic operators.- 8. The Lp approach to the Laplace operator.- 9. The p-Laplacian.- 10. The Rellich inequality.- 11. More properties on Sobolev embeddings.- 12. The Dirac Operator.

“The book is well-written … . The presentation is self-contained and unified. … The book will be of interest to graduate students and to all researchers in PDEs.” (Petar Popivanov, zbMATH 1436.35003, 2020)