With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.

1. Fundamental solutions and the Cauchy problem 2. The maximum principal and some applications 3. The first initial-boundary value problem 4. Derivation of a priori estimates 5. The second initial-boundary value problem 6. Asymptotic behavior of solutions 7. Semi-linear equations. Nonlinear boundary conditions 8. Free boundary problems 9. Fundamental solutions for parabolic systems 10. Boundary value problems for elliptic and parabolic equations of any order Appendix: Nonlinear equations Appendix bibliography Bibliographical remarks Bibliography Index