Krylov concentrates on the first boundary-value problem for elliptic equation and the Cauchy problem for parabolic equations, and addresses other issues such as Neumann and oblique derivative problems. With numerous exercises (and hints for their solution) throughout he covers certain second-order elliptic equations, tools from real analysis, certain basic estimates for parabolic and elliptical equations, equations with continuous coefficients, certain Sobolev embedding theorems, Fourier transforms and elliptical operators, and elliptical operators and certain spaces. Very interesting, especially in a textbook, is Krylov's material on equations with VMO coefficients and parabolic equations with VMO coefficients in spaces with mixed norms. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)