N. V. Krylov, University of Minnesota, Minneapolis, MN.

• ChaptersChapter 1. Second-order elliptic equations in $W^{2}_{2}(\mathbb {R}^{d})$Chapter 2. Second-order parabolic equations in $W^{1,k}_{2}(\mathbb {R}^{d+1})$Chapter 3. Some tools from real analysisChapter 4. Basic $\mathcal {L}_{p}$-estimates for parabolic and elliptic equationsChapter 5. Parabolic and elliptic equations in $W^{1,k}_{p}$ and $W^{k}_{p}$Chapter 6. Equations with VMO coefficientsChapter 7. Parabolic equations with VMO coefficients in spaces with mixed normsChapter 8. Second-order elliptic equations in $W^{2}_{p}(\Omega )$Chapter 9. Second-order elliptic equations in $W^{k}_{p}(\Omega )$Chapter 10. Sobolev embedding theorems for $W^{k}_{p}(\Omega )$Chapter 11. Second-order elliptic equations $Lu-\lambda u=f$ with $\lambda $ smallChapter 12. Fourier transform and elliptic operatorsChapter 13. Elliptic operators and the spaces $H^{\gamma }_{p}$

This book is certain to become a source of inspiration for every researcher in nonlinear analysis. [The book] is beautifully written and well organized, and I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of the modern nonlinear analysis."" - Mathematical Reviews